Are you in the uk? Over here we tend to use ring mains for socket outlets. I believe in other countries they tend to use radial circuits. We use radials here too but for less compared with ring mains, especially for sockets. With a ring main you essentially have a loop of cable running from the fuseboard to each socket (cable in and cable out) then returning to the fuseboard. The idea is to split the total load across two cables in parallel. With a radial circuit you have a single cable feeding one or several sockets without the return leg to the fuseboard.
Point is with a ring main if one socket works fine then the others should. All that can go wrong would be for the individual socket to fail (usually the switches give up or get crap and plaster dust in them) or for an individual socket to be connected with reverse polarity. No one socket would cause something to fail that’s plugged into it unless your socket has a poor connection or failing switch in which case the current could be cutting in and out which might cause surges especially with inductive or capacitive loads which have an initial spike in the form of a high inrush current at power on. Motors are a good example of this.
With a radial you’ve got the possibility of one circuit wired incorrectly and if it’s just one socket on that circuit you’d only have issues with anything plugged into that socket.
You say you’re moving to a new place… you should get the landlord to get a periodic test carried out if they haven’t done already. They’ll test ring continuity, polarity and earth loop impedance amongst other tests. This should put your mind at rest that the wiring is safe and everything works as it should.