Input lag is the down-side. Most TVs will process the image before it appears on the screen. This introduces an advantage for your opponent, especially in first-person shooter multi-player gaming if they will see things happening in the game before you do. It's something you have to consider in addition to the response time.
If you're not playing any games that rely on split-second timing (ie first-person shooters), a TV is probably just fine. Star Craft II seems like it would be a good one for the television.