The #1 problem with getting software demos early in the selection process (or as a replacement for the selection process, in most cases) is tunnel vision.
Software vendors train software resellers to demo only those features of their product that are (a) strong in relation to competition, (b) work well, and (c) are flashy. This biases the selection process in the direction of the features that look the best to the committee--even if it's a committee of one.
I've seen too many businesses select software that I knew would not meet their needs because they got tunnel vision. They focused on a few features that they didn't currently have to the exclusion of features they needed. It's one of the key things I wrote about in the Guide To Selecting Business Software. It's the key reason for having a selection process that includes needs analysis.

