A lot of the hats I've seen come out recently (particularly from the carnival tent/rewards) has been suited for a specific shape of graphic - these masks, for example, don't fit a lot of heads (they're narrow in the front view).
The accessories kind of have an issue with layers (the side view stuff maybe should appear behind the body) depending on the object this is more or less pronounced. The 'telescope' and 'chest' at the pirate day shop on sale right now are examples of this... it looks like they're hanging off the character's arm when used with a lot of the bodies.