Question concerning power outlet
As others have already noted, a picture with the cover help will definitely help with diagnosis.

Very likely there is no "new" problem, but the "old" problem is a real concern. Normally a receptacle is attached to a box by two screws - top &amp; bottom, and then the cover plate is attached to the receptacle by the middle screw. I see 3 likely scenarios (and there may be a combination):


The top &amp; bottom screws are loose (or nonexistent). If this is the case, tightening or replacing the screws should solve the problem.
The box that the receptacle is mounted to is loose. This is generally harder to fix as you may need to remove it and remount it properly or replace it with a different box.
The box &amp; receptacle are too far back, so the cover screw can't tighten properly. In this case, more likely the cover is moving than the receptacle. The solution to that problem is a box extender.


Once you have the cover off, you also want to check for:


Backstab connections. If you find any, you should switch to screw connections as they are more reliable.
Any signs of burning or arcing - e.g., charred insulation. If you have a loose connection combined with a shifting receptacle, you could easily end up with problems over time. If the receptacle itself seems damaged then I recommend replacing it - they are very inexpensive.