I get that error as well, try refreshing the page; as that worked for me the first time. It's not really a big problem as it goes away after a while. Should be noted that the message does not only show in your PM inbox, but virtually in many other areas of the forum including this topic for me. I am assuming you are reffering to the Error text in your screenshot which looks something similar to what I have on my screen, quoted below:
Happened to me too, but it honestly doesn't seem to do anything bad to our accounts to whick I've noticed Although someone should figure that out because that whole MySQL data or numbers or whatever could be killer to a hacker.