Without seeing an actual example of what you're citing...
I can say from personal experience that when I try to move a piece, and the game won't let me, it's because I'm placing myself in check....because I didn't notice a bishop lurking, usually.
If/when it happens to you again, take a good look at the position and see if that's the issue...and if it isn't, post it. I can guarantee that there are people on here that know more about it than I do! 
Ask yourself what possible incentive the chess.com team would have to program the game to be rigged against its user base.
No it is the new V3 software that still has a few bugs but there are support programmers always working on these issues as they come up. As you may have guessed the complexity of the web site is a coding nightmare. Plus sometimes a feature is added and another one goes haywire. Truly they work on these issues as fast as possible. We are really playing here to learn and have fun and companionship of members bound by the game of chess. It would be nice if you could get back a few points due to a bug of some sort but it would be impossible to implement.
Have you ever noticed somtimes on chess.com their is a piece that you cant move when playing a bot like you just cant move it because it wont let you for some reason then in the analysis it says that piece you couldn't move was a "missed win" and how somtimes you play beginner bots and they act more like master bots triking you into moving a pawn out of the way to kill one of their knights or somthing before they jump across the board out of nowhere with a bishop or somthing else killing one of your more important pieces and always managing to be in a position where they just bearly cant be killed and when you finnaly can they just move into a more impossible position and then check your king 10 times.