There are far larger plot holes in Part III. This is just a detail that they perhaps rushed along a little too quickly, but then again, maybe Michael could have pulled some strings and gotten him the role. Also, Corleone was a huge name in Palermo, so maybe the opera producers thought that having a Corleone in the opera would mean huge returns.

Who knows.

About the ages of characters in Part III... I imagined Anthony to be about 25 and Mary to be about 20. But if Anthony is 10-11 at his first communion in 1955, he would definitely be 30, or older, at the time of Part III.

Mary would be older than she was portrayed in Part III as well.