Replaying a game can be a let down, or an experience. Its cons would simply be the game dose not age well, or maybe it's not your type of game any more. Either way you can prevent neither. A truly good game should be able to beat all the odds. For me that game was Infamous, it never got old. Yeah there was a couple of animation problems, but nothing that crippled the game.
When you go back and play a game for the second time, it could potentially change your perspective of not just the game, but if your playing the third installment in a trilogy the entire series. Pending on the kind collectable can be a great part of replaying the game, for example Batman AA/AC riddles trophies kept me running back for more, but it only worked because your were working toward something, kind of like a side mission.