Another thing of note... I run mine (MacMini) headless as a server in a closet, I notice Safari, Chrome and FireFox all have issues and lock up in addition to the LMI issues. However if I plug in a monitor then all the issues go away and it functions fine. Very strange!
I, too, am anxiously awaiting a resolution to this issue. I have removed and reinstalled LogMeIn, but still am unable to access my Mac from another LogMeIn client. Interestingly, I *can* access other computers from my Mac, but not the reverse. Basically, my user name and password gets rejected each time, even though it is assuredly correct.
I've been using a work around with SSH that helps. Once you get knocked back into that login screen and you can't connect, paste this script into an SSH client (Secure Shell client on Windows or terminal on a mac)