Absolutely nothing.
I have a Zeiss conquest 3-9X40 on one of mine.
In fact every .22 that I have a scope on, has what would be considered a centerfire scope on them.
Not much other than most rimfire scopes have fixed parallax at 50 yards and most centerfire scopes either have it fixed at 100 yards or have adjustable parallax.
As previously stated, looked at the parallax specs on the scope. Some are setting for adjustable parallax down to 10 yards. Others are set much farther.
Also, some rimfire scopes are set with non-adjustable parallax at 50 yards. If you plan to shoot farther, this becomes an issue.