Well, that didn't go super smoothly, got prompted a number of times with system warnings and here is the tail of my output:

Examining /etc/kernel/postinst.d.
run-parts: executing /etc/kernel/postinst.d/apt-auto-removal 3.16.0-37-generic /boot/vmlinuz-3.16.0-37-generic
run-parts: executing /etc/kernel/postinst.d/dkms 3.16.0-37-generic /boot/vmlinuz-3.16.0-37-generic
Error!  The dkms.conf for this module includes a BUILD_EXCLUSIVE directive which
does not match this kernel/arch.  This indicates that it should not be built.
Error! Bad return status for module build on kernel: 3.16.0-37-generic (x86_64)
Consult /var/lib/dkms/synaptic-i2c-hid-3.13.0-32-backport/1.6.1/build/make.log for more information.
run-parts: executing /etc/kernel/postinst.d/initramfs-tools 3.16.0-37-generic /boot/vmlinuz-3.16.0-37-generic
update-initramfs: Generating /boot/initrd.img-3.16.0-37-generic
run-parts: executing /etc/kernel/postinst.d/pm-utils 3.16.0-37-generic /boot/vmlinuz-3.16.0-37-generic
run-parts: executing /etc/kernel/postinst.d/update-notifier 3.16.0-37-generic /boot/vmlinuz-3.16.0-37-generic
run-parts: executing /etc/kernel/postinst.d/zz-update-grub 3.16.0-37-generic /boot/vmlinuz-3.16.0-37-generic
Generating grub configuration file ...
Warning: Setting GRUB_TIMEOUT to a non-zero value when GRUB_HIDDEN_TIMEOUT is set is no longer supported.
Found linux image: /boot/vmlinuz-3.16.0-37-generic
Found initrd image: /boot/initrd.img-3.16.0-37-generic
Found linux image: /boot/vmlinuz-3.13.0-52-generic
Found initrd image: /boot/initrd.img-3.13.0-52-generic
Found linux image: /boot/vmlinuz-3.13.0-37-generic
Found initrd image: /boot/initrd.img-3.13.0-37-generic
Adding boot menu entry for EFI firmware configuration
done
Setting up linux-image-extra-3.16.0-37-generic (3.16.0-37.51~14.04.1) ...
run-parts: executing /etc/kernel/postinst.d/apt-auto-removal 3.16.0-37-generic /boot/vmlinuz-3.16.0-37-generic
run-parts: executing /etc/kernel/postinst.d/dkms 3.16.0-37-generic /boot/vmlinuz-3.16.0-37-generic
Error!  The dkms.conf for this module includes a BUILD_EXCLUSIVE directive which
does not match this kernel/arch.  This indicates that it should not be built.
Error! Bad return status for module build on kernel: 3.16.0-37-generic (x86_64)
Consult /var/lib/dkms/synaptic-i2c-hid-3.13.0-32-backport/1.6.1/build/make.log for more information.
run-parts: executing /etc/kernel/postinst.d/initramfs-tools 3.16.0-37-generic /boot/vmlinuz-3.16.0-37-generic
update-initramfs: Generating /boot/initrd.img-3.16.0-37-generic
run-parts: executing /etc/kernel/postinst.d/pm-utils 3.16.0-37-generic /boot/vmlinuz-3.16.0-37-generic
run-parts: executing /etc/kernel/postinst.d/update-notifier 3.16.0-37-generic /boot/vmlinuz-3.16.0-37-generic
run-parts: executing /etc/kernel/postinst.d/zz-update-grub 3.16.0-37-generic /boot/vmlinuz-3.16.0-37-generic
Generating grub configuration file ...
Warning: Setting GRUB_TIMEOUT to a non-zero value when GRUB_HIDDEN_TIMEOUT is set is no longer supported.
Found linux image: /boot/vmlinuz-3.16.0-37-generic
Found initrd image: /boot/initrd.img-3.16.0-37-generic
Found linux image: /boot/vmlinuz-3.13.0-52-generic
Found initrd image: /boot/initrd.img-3.13.0-52-generic
Found linux image: /boot/vmlinuz-3.13.0-37-generic
Found initrd image: /boot/initrd.img-3.13.0-37-generic
Adding boot menu entry for EFI firmware configuration
done
Setting up linux-image-generic-lts-utopic (3.16.0.37.29) ...
Setting up linux-headers-3.16.0-37 (3.16.0-37.51~14.04.1) ...
Setting up linux-headers-3.16.0-37-generic (3.16.0-37.51~14.04.1) ...
Examining /etc/kernel/header_postinst.d.
run-parts: executing /etc/kernel/header_postinst.d/dkms 3.16.0-37-generic /boot/vmlinuz-3.16.0-37-generic
Error!  The dkms.conf for this module includes a BUILD_EXCLUSIVE directive which
does not match this kernel/arch.  This indicates that it should not be built.
Error! Bad return status for module build on kernel: 3.16.0-37-generic (x86_64)
Consult /var/lib/dkms/synaptic-i2c-hid-3.13.0-32-backport/1.6.1/build/make.log for more information.
Setting up linux-headers-generic-lts-utopic (3.16.0.37.29) ...
Setting up linux-generic-lts-utopic (3.16.0.37.29) ...
Processing triggers for libc-bin (2.19-0ubuntu6.6) ...

It appears that the new kernel images WAS built, so I am going to reboot and see what happens.

There are several ways to install kernel 3.19 on Ubuntu 14.04. Here's how I did it on my desktop - 3 commands:

sudo add-apt-repository ppa:canonical-kernel-team/ppa
sudo apt-get update
sudo apt-get install linux-generic-lts-vivid

I'm no expert, and I don't know if this will work on the XPS-13. But it was simple and worked on my desktop.

Just to clarify, the PPA used for the vivid lts kernel above is for testing kernels:

https://launchpad.net/~canonical-kernel-team/+archive/ubuntu/ppa

The "official" Vivid LTS kernel is due some time in September

So this worked...I am amazed.  I might restore to factory defaults to see if a direct upgrade will solve these issues as well.  Here is my final status:

gshulegaard@ronin:~$ lsb_release -a
No LSB modules are available.
Distributor ID:    Ubuntu
Description:    Ubuntu 14.04.2 LTS
Release:    14.04
Codename:    trusty
gshulegaard@ronin:~$ uname -a
Linux ronin 3.19.0-17-generic #17~14.04.1-Ubuntu SMP Thu May 7 11:05:22 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux
gshulegaard@ronin:~$

- Graphics problems are fixed, there is no more choppy Unity performance.

- Trackpad issues (Two-finger click-and-drag, Right click) ARE working.

- Palm rejection is working better, although is still annoying enough that I (and I think most others) will disable tap to click.

- Keyboard keystroke issues are less fequent, but are still occasional.  I have seen repeating keystrokes 1 time so far...so they occur far less, but I am troubled by the fact that they still occur.

The magic command(s) for other distressed XPS 13 users are just as MRC01 suggested:

sudo add-apt-repository ppa:canonical-kernel-team/ppa
sudo apt-get update
sudo apt-get install linux-generic-lts-vivid

I am debating resetting to factory settings and trying this from the start...just to see what happens.  If I do, I will update here.

Here's my lsb_release on the desktop on which I did this

LSB Version:    core-2.0-amd64:core-2.0-noarch:core-3.0-amd64:core-3.0-noarch:core-3.1-amd64:core-3.1-noarch:core-3.2-amd64:core-3.2-noarch:core-4.0-amd64:core-4.0-noarch:core-4.1-amd64:core-4.1-noarch:security-4.0-amd64:security-4.0-noarch:security-4.1-amd64:security-4.1-noarch
Distributor ID:    Ubuntu
Description:    Ubuntu 14.04.2 LTS
Release:    14.04
Codename:    trusty

Here's my uname -a

Linux se-mclement-Z400 3.19.0-17-generic #17~14.04.1-Ubuntu SMP Thu May 7 11:05:22 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux

Well, I went ahead and did a factory reset and upgraded the kernel, here is a thead about it:

http://en.community.dell.com/techcenter/os-applications/f/4613/t/19632562

At this point, my wireless is not working, but everything else seems to be functioning as intended/well.  I am waiting on Dell to get back to me with how to restore wireless networking and will update the other thread as soon as I have that fix.

Also, wireless IS working.  I updated the other thread with how to fix it and also with an upgrade path that avoids having wireless break.

Dantesrequiem, other than WiFi, how has the XPS been working with the new kernel? Does it utilize more CPU capabilities than previously (I remember reading about not being able to throttle up the processor)?

Tbh, I am not sure what processor issues people were having before.  I remember someone saying that frequency stepping wasn't working, but mine was out of the box.

That said, CPU stepping and throttling up seem to be working.  I can monitor the frequency steps with [watch -n 0.1 'lscpu | grep "CPU MHz" '].  Since the upgrade I have also put the machine under load and have had the fans kick on for the first time.  I believe 3.19 had Intel chipset drivers in it since the performance of the integrated graphics have also improved significantly.

That's great to hear. Has there been any effect on battery life now that better drivers are in use?
I wouldn't be surprised if the key repeat issue is something within the code of Ubuntu itself. Even with key repeat settings disabled, I still get it to show when using the arrow keys to move around in Google Maps on my M4800.

I haven't noticed much difference in battery life...but I was impresssed with it before I upgraded the kernel so I haven't really been paying attention to it much.

I use my personal computer at work, I come in at 9 AM and can use it off battery until ~2 PM (not including a lunch break since I take lunch at my desk).  I have the Dell Power Companion, so with that helping out, I can usually go a full day 9 AM - 6 PM without needing a charge. But my typical use of this machine is just coding. I am not typically putting the hardware under load (I code in Emacs then deploy to a cloud server with Git).  The biggest power draw is definitely the screen...and I have the 4K version so it's a power hog.  Still 5 hours average on a full charge + 2-3 from the Power Companion is pretty good in my book.

I am not sure the key repeat issues are from Ubuntu.  In fact, because you are seeing key repeats even after disabling repeats indicates to me that the repeats are actually being sent through the drivers as duplicate, separate key presses.  I also have System76 Galago UltraPro and I have never had key repeat issues.  If anything, I suspect it has something to do with the kernel drivers for the keyboard connection.  But I can't be sure.

They are very infrequent though, almost not worrying about at all.  I have been using this machine for a solid hour now and haven't seen it.

<< Has there been any effect on battery life now that better drivers are in use? >>

Here's a good reference to managing power & battery life on Linux - most of this is directly applicable to Ubuntu. I would run the XPS-13 "as-is" with the 3.19 kernel first, to establish a baseline. Then if you want to try extending it further, try TLP or Laptop Mode Tools.

wiki.archlinux.org/.../Power_management

Thank you all for your help. I think I'm about ready to pull the trigger. I'm carefully watching Dell's site as the price has increased, but there is still currently their "Instant Savings" that keeps the price where it was before. Hopefully I can get it ordered before that goes away and the machine becomes another $100 more expensive.

Thanks again for everybody's input so far. I have just received my XPS 13 DE. I bought the 1080 non-touch with 256 GB SSD. This machine is built really well, and very light. I haven't experienced any key repeat issues yet. The touchpad is working well, but it doesn't right click with one finger. I believe the newer kernel fixes that.

What I'm trying to do right now is create recovery media before I upgrade the kernel and install my programs. The Dell Recovery program keeps crashing when trying to write to "raw" media. Ubuntu is recognizing my flash drive, though. Are there any tricks to doing this? I accidentally skipped it when running the initial setup.