I say no. Here’s the thing: like/dislike/upvote/downvote/whatever systems seem good on paper, and if used the way they’re intended can work. The problem is people. Take reddit, for example. For those of you unfamiliar, reddit uses a system where you can upvote or downvote posts which moves them up or down, making them more or less visible. Now, in theory, the system is meant to be used to bring good information to the forefront, and get rid of bad information. The problem is that it winds up being used as an “I agree/I don’t agree” system. As a result, subreddits tend to become echo chambers. The same popular opinions get upvoted over and over and if you post anything that goes against the popular opinion, you get downvotes into oblivion. This results in subreddits becoming extremely one-sided, as people feel bullied into not posting anything that goes against the grain. This is unhealthy to any sort of forum.
So no. Like button is a bad idea.