EDIT: I noticed the first paragraph was removed from my post. Basically I'd been having this issue on my Surface Pro 3 for a few months in the tech preview, but it seemed to go away after going to official release. It's happened maybe twice since release on my Pro 3.
However, I've just upgraded my girlfriend's Surface 3, and she says she has the same problem very regularly. It's obvious touches are being detected as right clicks as jump lists open on the task bar, and the touch indicator is a square.
Performing an actual right click does not fix it, nor does locking and unlocking the device. Pen inputs are shown, but have no effect during this either. The only foreseeable method of fixing it is a restart.
I haven't found any other posts on this issue, but the fact it's affected both of us is very strange. I can provide video of the issue if needed.
I do hope someone has some insight into how to solve this problem. Thanks.