Having devoured hot pursuit:
It seems to me that there is a major thing I think needs more attention and a minor thing.
The major thing is spellcasting (mainly speaking of On Foot here). The prevailing assumption is that everyone is going as fast as they can. There are no rules to run and cast in the standard D&D rules, but there aren't rules to run and attack either, so you think that would be a common enough activity it might deserve some special attention.
Possible house rule add-on here is that you might be able to slow down and cast (losing ground on your opponent) or there might be a cast on the run feat that lets you do more. One hand on the wheel sort of covers this, but I think there should be a concentration check in there somewhere. Further, you have to consider spell ranges (though matching it up to the existing range categories seems easy, I would almost want to tack on the range modifiers to DC or require a touch attack roll to hit a moving target.)
The minor thing is feats. Some comments on RPGnow seem to be interested in new feats. I can mostly rip off Spycraft (I don't expect my PCs to take them, but there are action points), but I am really more interested in what the impact of existing feats like Shot on the Run or Mobility might be. I'd definitely think someone with mobility chasing on foot would get a bonus to swerve checks, for example, and someone with shot on the run would get some sort of bonus when firing while running.