I just got out my old, well used, Model 101, 20ga. late '60s Skeet gun. Took the forearm off and there is NO wiggle at all. It does open very easily, as most well used ones do, however that does not mean they are loose.
If the gun in question is truly loose, it must have been abused a lot by slamming it shut! A lot of people have no respect in how they handle and close a O/U or SxS.
If it is tight when the forearm is on, then shooting it will not do any damage.
You might check for wear on the locking plate.
If your still afraid of it, have a GOOD gunsmith, repeat, GOOD gunsmith, look at it.
I respect eightbore's opinion, but I would not suggest putting it in a vice and squeezing the sides together.