Firstly, your semen will be fine if you left the plug out and the tank was full. All of the semen should have been sitting immersed in liquid nitrogen.
If the tank had less nitrogen there could have been an issue with the semen in the top goblets getting a little warmer, but that would have depended on how full the tank was exactly.
Secondly I don't know of a way to guarantee that semen is good unless you put it under a microscope. When I have had concerns about a tank I just thaw a straw of a less desirable bull and check it. Maybe not a bad thing to do - keep some semen you might not use again as a check on the tank. You can also get vials with die in them that change colour if the tank is thawed.