I have pretty much the same problem as in Dell XPS 13 9350 with Ubuntu 15.10 - Touchpad freezing, jumping - but on Ubuntu 16.04.
My touchpad stops working randomly, or can work somewhat only if I click and drag with it. Sometimes it starts working if I do a two-finger scroll, but this doesn't always work.
I have installed a mainline kernel (version 4.4.13-040413-generic) to fix an issue related to resuming after suspend. However, the present touchpad issue was present on a vanilla 16.04 install too.
Any help is appreciated. How would I even begin debugging this? (I am not shy to use the terminal or modify my system, as long as I know how to bring it back to a working version, in case the experiment fails).
I had the same problem when I put Ubuntu 16.04 on my Dell XPS13 (9350). For me the problem was largely resolved by installing libinput:
The only issue I have now is that the mouse pointer freezes once in a while. But this is very rare and I can always unfreeze it with a left click. Overall I'm very pleased with the improvement libinput has made to the performance of the touchpad.
You can read more about this solution at https://askubuntu.com/a/678122
J-Linux
I have experienced the same issue on my XPS 13 9350. I had the same issue about a year ago on my XPS 14 L421X. Dell updated the BIOS and then it was solved.
I had a more extreme version of this issue on my XPS13-9333. After the update from the pre-installed 14.04 to 16.04, I had no touchpad anymore. Nothing would bring it back.
Updating the BIOS as per these instructions magically brought it back to life