I interpreted the fact that he was reviewing multiple copies of the same text as him searching for Galileo’s notes, but I suppose it’s possible that the motivation was the possibility of discrepancies between printings.
The Almagest was hand written about 1400 years before Galileo lived, so it's not so much looking at different printings as at different editions that are based on different set of copies of the copies of the copies etc, further many editors would try to "fix" the ancient work, removing material they didn't like and adding their own stuff or material from other works... it can get very messy.
Owen Gingerich was a historian of astronomy who did a census of printed early editions of Copernicus' book De revolutionibus. He found a tradition of students copying annotations from teachers readings into their own copies of the book. I recollect that he was able to trace various traditions of commentary each stemming from a well known astronomy teacher.
I suppose that checking early printings of key works looking for annotations is a pretty standard thing to do now.