Two main possibilities there: Scotty's impromptu repairs didn't hold and there was damage from the attempt to sail to help the crew of the Reliant (which we don't see aboard Kirk's ship at any point), or they did hold and the ship entered another adventure that involved damage.
Both are unsatisfactory in more ways than one. Kirk says they have repaired damage and reassigned people, but why did this happen in deep space when the ship was mobile at the end of the previous movie? Why didn't they first sail home, then repair and reassign? Kirk got to Regula on a joyride he wasn't even supposed to be taking - it can't have been all that far away. The capabilities of the ship don't well match either a scenario of staying still until repaired, or swashbuckling with new adversaries.
On the other hand, the fault could be all ST2's. There is damage to the port side of the secondary hull there, as seen in Spock's damage control schematics - but the final scene of setting sail for Ceti Alpha fails to show this damage. OTOH, the starboard side is not seen at the end of the movie, and could have accumulated more damage since last seen (long before the nebula fight); it won't be seen properly again until the ship faces Kruge's BoP, but the "extra" damage is consistently there in earlier ST3 shots as well.
Timo Saloniemi