Initially, a loose screw will produce heat under load, in all devices, which are not designed to consume power. So, any switch, receptacle and even circuit breaker should not feel hot to-the-touch and should be your first suspect. If you have a 3 lamp tester, do what I do, insert it in the receptacle and wiggle it around. If lights dim you've found the bad one. In some cases, it may not even look bad, but should be replaced.
If a loose connection has progressed to the point that an arc-over has occured and welded back, when power flows in the connection and at a later date it may "glow" red hot, further destroy the connection and often start a fire. The "glowing connection" is hot enough to melt all plastics and ignite wooden studs. It is the worse possible electrical condition there is.
Combination Arc Fault Current Interruptors (AFCI) circuit breakers have been required in all new installations since 2011 and are designed to trip when such conditions are detected. Unfortunately, it's a very difficult task and many electricians don't believe in them.
Although they cost about $40 each, you may want to insist that an electrician install them on all 120V 15A and 20A circuits in your panel, especially with the problems you've described.