I haven't really done much 3.x pbp (mostly play MnM here), so I can't offer much in the way of comparison.
However, a standard combat for 13th level (encounter level = party level) took about a month to resolve. It wasn't the fastest posting rate I've seen, but we were still moving things along pretty quickly IMO.
Problems... I think the biggest problem is that teamwork is significantly more important in 4e during combat, as opposed to setting up buffs. So coordination is a problem - working out even something simple in combat could easily double the time between posts.
Keeping track of everything can be tough - I just forgot to use the AP on now deceased Stormrage Shambler, I think I forgot its damage bonus when bloodied too. In tabletop, it's easy to forget things in the moment. On the other hand, in this game, my concentration is often off simply because I came up with all everything months ago. Not really an edition specific problem though.
Interrupts and other out of turn actions are tough to handle. I think that the PCs have missed a few good opportunities to use some of their powers (like Shield) because it's rather clumsy to respond like that. It'd take like 2 seconds to handle face to face. Late 3.5 had its immediate actions too though.