It's hard for weak players to tell if a game is good :) How do I know if an anonymous game was between IMs or world champs? I can't tell :p
An interesting game to me has what I would consider a creative idea played by either side. Of course to a professional that same idea may be normal stuff, but if I've never seen it before, or see it in a different context I may find it interesting :)
As an example once I was looking over a game where in the endgame the GM set all his pawns on the same color as his bishop, what's going on? Then you see that he was playing for restriction of his opponent's pieces and ground him down in an endgame where the result was never in dispute. And so I learned an exception to the standard idea of not setting your pawns on the same color as your bishop.
Another game may include advancing the pawns in front of your king as part of a winning attack. To a professional this is probably so obvious it's dull, but certain exceptions (or things I haven't though of) are interesting to me.
A GM sacrifices a piece for nothing? What's going on? Then you see his other pieces coordinate beautifully and his opponent is somehow lost. Things like this are a lot of fun :)
when you look over a game what qualties do you look for to see if it is a good/intreasting one ?