I had worked for AAI for a number of years. Prior to that, I worked at a "real" airline and subsequent to AAI I worked at a "real" airline.
I will say anything that was written up in the logbook was generally fixed. However, the key is, if it was written up! I have seen MX go ballistic when a pilot wrote something up that couldn't be fixed. If my memory serves me correctly, TF-ATF was written up with a bad rudder ratio changer a few years ago in JED. It sat for a few days because the Captain who wrote it up wouldn't change his write up. So, parts had to be flown into JED and clear customs, all of which takes time. I do know MX and Iceland did put a great deal of pressure on the Captain to change his write up.
As far as ICAA goes, i wouldn't call them the best judge in the world. Look what has happened to the validation issue. The validation process in place is not what the JAA intended or wants. However, it still goes on.
Anyhow, AAI is a job, I still have friends there who I encourage to leave, some have and some are quite content. It's really a personal decision. For me, there was no decision at all, a "real" airline is much more enjoyable and much safer!!!!