Thanks for the suggestion.

I performed the ePSA Diagnostic Quick and Advanced (with "Thorough mode" enabled) tests, with no errors found. 

Although it should be mentioned that while ePSA does have an interactive keyboard test, there does not appear to be a diagnostic test that evaluates trackpad input.

Hello,

Run ePSA diagnostics outside of Windows with the laptop powered off press the power button and when the dell logo appaers repeatly press F12 in the menu choose diagnostics if you receive an error and validation code make a note of them.

I should have probably mentioned that I purchased this Inspiron from Dell Outlet.  I'm starting to think I may know why it was previously returned. 

If you meant you can replicate the issue by applying pressure on Palm-rest (without touching the pad) than no point Troubleshooting. There is no such settings in windows or BIOS which can start this kind of behaviour. Multiple parts can be faulty, Palm-rest Touchpad or bottom base itself.

Seek a Palm-rest replacement : Would take around 2 days

OR

Seek a new system exchange : Would take same time as buying a new computer.

Depending the urgency choose your option accordingly.

Thanks for the thoughts.

I cannot consistently replicate it.  The issue occurs randomly, sometimes after short usage (within minutes of powering on) or other times after an hour or two.  Once it begins happening, the erratic mouse movement and clicks continue without any physical interaction with the trackpad or chassis.  In the videos, I interacted with the trackpad just to move the mouse pointer to where the issue could be better visualized, i.e. hovering the pointer over the Firefox icon to see multiple browser launches due to repeated double-clicks being registered.

At this point, I think software/driver troubleshooting has been exhausted and this is likely a hardware issue, so I'll have to open a case with Dell.

Thanks to everybody for the assistance.