File mover Arjoopy runs into the rate limit here after 16 legitimate moves. Commons is rather different from other wikis, we may move tons of file pages in a short period.
As I don't know exactly what rate limit is tied to, the most neat solution would be to increase the move limit for filemovers
or, if that's not possible, increase the move limit for autopatrollers, patrollers and image reviewers. (file movers are typically in one of those groups as well)
As for the number, I'd say increase it to 100 per minute or so. File mover
/autopatrol/patrol/image reviewer are all only assigned by humans, so only trusted users get those rights.
Edit: I understand the rate limit for moves can be adjusted for just file movers.