I don't think that hurts you at all, it just gives you exposure to more of the residents. I think a lot of places even if your rotation does not straddle the team switchover date they have the students spend two weeks on one team and then send them elsewhere just to see more of the program. I would look at it as an advantage really. If you spend your whole month with one small set of residents and one to three attendings, then it is harder to get a true feel for the program as a whole. That was one problem I saw at your home program: you spend the whole month with one pgy-2 and one pgy-4 or 5 and the other twenty residents you only see at conferences and at spine clinic (where they all have to go every week except for the hand team). If you want a letter from a certain attending you better request ahead of time to be on that team because you won't get time with the others (particularly the big guy who won't even consider writing your letter unless you are on his specific service).
At loyola I spent two weeks at the VA with three attendings then two weeks on hand with two others. At the end I felt like I could have easily gotten two or even three letters out of it if I had wanted them (already had enough and it was pretty late in the application cycle so I didn't ask for them). Two of them actually offered though.
Hope that helps.