Playing Walking Dead on PC here, though on my TV with a 360 controller. Works fine. PC version is also, I understand, not afflicted with the game-breaking save game bug that has mangled some players’ progress. To be safe, play through whole episodes in a single sitting if you can. They’re about 2-3 hours tops each, so it’s more than doable, and they’re clearly designed to be played that way.
I finished it tonight. I won’t say anything else for fear of spoilers.