As of yesterday my side view mirror on the driver's side seemed to be OK but this morning while driving I noticed it was "flopping around". When I'd take off, it would collapse toward the vehicle, and when I'd stop it would flip outward facing traffic.

Once I got to work I checked it out and it looks like there's a pin or something it rests on but it's not keeping it in place. There are no screws that appear to have fallen out.

Is there an easy fix for this or will I have to replace the whole thing?

Better replace the whole thing... Since you said that it has no screws on it...