The outlet in one of our bedrooms is such that when you wiggle a plug
in it the power to the plug goes on and off. Experienced that many
times, but what's odd, to me, is when the power is disrupted by
wiggling it, it also cuts out the power to the overhead light/fan,
which is operated by the switch at the door.

There are two switches by the door, one of which is controls the
switching of some/all of the outlets, but that switch is taped ON, so
not a factor in this. When I move the outlet, with it pulled partly
out of the box, the power goes on and off, so there's a loose
wire/connection in the outlet. Question is, based on what's happening,
can you tell if it's a specific wire? By pulling (with power off) I
can't tell that one is loose. Or should I be replacing the outlet?
Thanks.