Screw pops or nail pops
aren't usually too serious, but if you see a lot in your ceiling I would definitely look into fixing them. Like you said, the screw isn't tightly fastened to the frame. This means the screw isn't holding the drywall to the stud. They're fairly easy to repair.
To fix screw or nail pops, you need to drill a screw into the drywall one or two inches above the nail pop to re-secure the drywall to the stud. You also need to screw below the nail pop as well. Be sure to sink the screws below the surface of the wall. You don't want the nail or screw to be sticking out. After that, you just have to finish the holes.
If you don't want to do it yourself, you can get some drywall guys to come and fix it for you pretty easily. Hope this helps!