I've had a problem for a while with SMB3 sprites showing up in front of the background when they shouldn't. This is primarily true when there are objects coming out of boxes or pipes, like mushrooms or pirrana plants, not when Mario goes behind the scenery in the title screen or elsewhere.
I just noticed recently that the Nesticle changelog mentioned fixing SMB3 sprite priority problems, so I'm hoping that maybe someone else has had the same problem and can recommend a solution. I also get a similar problem in Castlevania, where you first enter the castle he walks in front of the wall instead of behind it.

Offtopic, I've been coming to NESDev for a long time and just noticed the messageboards today!

-hcs