It depends. If the conenction was loose and you repaired it then no problem. If the circuit is over fused then could be big issues. The wires in the walls could be melted.

Yes, you need to have a reliable electrician look at this. This is not normal, and you could end up with a house fire. Something is not right here. I don't mean to be alarmist, but you should not be comfortable with this until your whole wiring system is inspected and possibly fixed: that means the breaker/fuse box and the sizing thereof, the type and adequacy of the wire gauges, the integrity of the connections between the wiring and all the receptacles, etc. Many home inspectors are not necessarily good at finding things hidden in walls or doing close inspections of the electrical system, so that doesn't make me comfortable.

I would have been pulling every device in the house and checking for at least tight screws and aluminum wire after the first incident.

Over long periods attachments that were not tightened correctly often work loose.

Just plain old temperature cycles from day to night can loosen less than optimal connections.

Torque specs have only created much attention in the past few years for devices. Large panel connections have had them for a long time, but I cannot recall an AHJ with a torque wrench (or torque screwdriver) until about 4-5 years ago.

The numbers for device screw torque are surprisingly high to many folks.

Thanks for the responses. I don't think anything was loose, but it's possible I missed something. As for the wire, everything I've seen has been copper. In general it's a very well-maintained house, but maybe within the walls things are sketchier. Guess I'll have to have someone come check it out.