I have about 15 of these at the moment that have the same issue. Samsung is no longer covering these under our warranty. I took one of them apart today and got the entire trackpad assembly out. I did it without a heat gun, but I would imagine that with a heat gun it would be a ton easier. Anyways, to kind of comment on cparrish's post, I was also told by a Samsung support person that there was a spring under the trackpad that could be cleaned. This "spring" that they are talking about is a metal dimple switch pad, and if that were actually bad, no amount of alcohol would fix it. This dimple pad is pressed against a raised plastic cross ( + ) on the plastic under the trackpad. And as for cparrish saying that the trackpad is glued in is not entirely true. It is just held in by some strong double stick tape that can be loosened with a heat gun. If using a heat gun though, take extra care not to overheat the plastic and warp it. The heat should ONLY be applied to the under side of the pad. Heating the top of the palmrest will not get enough heat to the tape to loosen it.
What I found in all this is that the trackpad apparently works it's way forward and gets wedged on the frame of the palmrest plastic. After the trackpad is removed. re-install it by pushing the back side of the trackpad (not the underside by the tape) as much as you can to butt it up to the palmrest plastic closest to the keyboard. This should leave enough of a gap on the front side of the trackpad where it won't catch and allow it to freely move and click.
Hope that helps people as this seems to be a VERY common issue with the XE303C12 model chromebooks from Samsung.