My daughter skipped 2nd and 6th grades (and is now in 7th). There were pretty much 0 issues with the first skip. The kids were not that much older than her, and she was in a small school with small class sizes.
I would say we've noticed some social issues with the second skip. Nothing horrible, but my daughter does feel slightly out of step (socially) with her classmates. At the school dance, she brought a book and read under a table the whole time, and she has made comments about her friends getting a little boy crazy. She has gotten teased a little bit about being a "know-it-all", but that came from the kid who was previously the "know-it-all" in the class she skipped into.
Sports at the middle school (combined 7th and 8th grade teams) have been a mixed bag. She was fairly out-sized in soccer; had some limited success in swim; and lost a lot, but had loads of fun, in tennis.
Academically, we are happy with the skips. 7th grade has been slightly challenging at times (mainly filling in the gaps in math) but for the most part it has been easy enough that I cringe to think how bored she would be in 6th. Luckily 8th grade will involve some subject acceleration as well.
One of the more frustrating things has been coordinating summer activities. Some camps go by last grade level, some by next grade level, and some are by age. My daughter was mildly upset to find out that a camp she loved last year is now closed to her because she skipped through the last grade they accepted.
Best of luck to you,
-S.F.
