[Nate tha' Great]

I think you can consider checking behind on the river especially if he's passive enough to play an ace with a weak kicker this way but betting isn't a huge mistake.

His play was fine except for his preflop limp. A more aggressive line on his part would probably have folded out a 9, which he doesn't really want to do, and wouldn't have done him any good if you did in fact have an ace.