I have three 624s, 3", 4" and 6-1/2".
Two of the three were in the recall serial range.
Coincidentally, both of them needed sideplates replaced and went back to S&W. Both passed scrutiny and were repaired and returned.
Before sending them in, I read every scrap of discussion that I could find.
My conclusion was:
Both of these guns had been shot - a lot - before coming to me.
They had not failed structurally any any way whatsoever.
I have never seen, or even heard of, any 624 failure of any sort.
I don't hot rod my .44 Specials. Have plenty of 66 Magnums for that job.
Conclusion:
I would shoot any S&W 44 Special revolver with SAAMI-spec ammo and not worry in the slightest.
As for sending it in, wouldn't do it unless other work was needed.

That's my decision. Its your gun, you will have to make yours.

Last I heard, the (very few) replacement guns were current production 629s.

__________________
-jwk-
US Army '72-'95