The stove suddenly quit working, with only the broiler still working. Upon investigation, the 3 prong stove outlet prongs inside of the outlet appeared to have been spread apart too far so the 3 prong stove plug-in was no longer making a good connection. He pushed the prongs inside the outlet closer together, now there is good contact again with the stove plug. But should I replace the outlet for safety? And What would cause the outlet prongs to spread apart inside of the wall? My feeling is the stove must have been unplugged by someone and then not plugged in correctly or jammed in or maybe when it was pulled out from the wall for cleaning, it was yanked.
3-prong outlets are obsolete and very dangerous. Specifically, the appliance industry lobbied NFPA to allow bootlegging ground on dryers and ranges, on the logic that these sockets are rarely disturbed. However, This means an ordinary failure in the neutral wire electrifies the chassis of the appliance.
As such, any failure in a 3-prong appliance cord is nothing to trifle with. It should be replaced, both socket and plug, with all possible urgency.
Now, if upon removing the socket, you discover there actually is a ground wire there*, or if there is metal conduit which provides ground, or if it is easy to retrofit a ground wire via any viable route, or if you are willing to fit a GFCI breaker on this circuit which moots ground... In any of those cases, you should seize the moment and upgrade to a 4-prong plug and socket. Part of this is removing the neutral-ground bootleg strap in the appliance.
If you use the "not actually grounding it but fitting a GFCI breaker" approach, mark the socket "GFCI Protected/No Equipment Ground".
These sockets are not designed for (not strong enough for) frequent swapping. If you have a reason to be frequently swapping this plug, then ask a new question about your reasons for doing so, and if there is a better way to do this (there is).
* It happens all the time where a house is built with a 4-prong socket, and the appliances arrives with a 3-prong plug, so the builder changes the socket to 3-prong since modifying buildings is his bailiwick, and modifying appliances is not. Later a new appliance is purchased, and the installer changes the 4-prong plug to a 3-prong (instead of restoring the 4-prong socket) because modifying appliances is his bailiwick, and modifying buildings is not.
I would replace the outlet. For whatever reason the outlet wasn't making contact with the plug. The "jaws" of the outlet can soften up because of age and heat generated from the current flow. Pushing them closer together is just a band aid and they will probably spread apart again causing some arcing ... during Thanksgiving day or Christmas. Good luck. Also take a good look at the plug. If it looks burned or scorched replace it too.