I have the exact same problem. It is making LogMeIn unusable. It does seem to be dependent on which machines I control (strangly, newer machines are worse).
I found the npRACtrl.dmg file on my computer but if I inspect the DMG file and look at the plist.info file it has the version string "1.0.660 Copyright (c) 2003-2012 LogMeIn, Inc." So it seems to be version 1.0.660. Does anyone else show this? Installing it also did not fix the problem.
To see the version information: Double-Click on the DMG file to mount it. Open up the LogMeIn Client Installer.pkg file by right clicking and "Show package contents". Open the folder "Contents" then Double-Click info.plist.
With so many users reporting this problem, it is untenable to say that it is difficult to reproduce. The "fix" needed is obvious: rescind the broken version of LMI and "upgrade" EVERYBODY back to the old version. THEN go in and try to fix the issue. LMI today, and for months now, is completely broken and unusable, so to persist with the new broken version of the software is a very bad decision.
At the very very least, LMI should offer the upgraded older version as a download for users that need it.
I chatted with LMI Help and they gave me this link to a previous version of LMI. This upgrade-downgrade did drop my CPU usage from 100% to 15%, and although I am still experiencing bad lag, it's hard to say whether that is LMI's fault or the fault of my connection across the internet.
It is January 10th 2013 and I have Mountain Lion on my new MacBook. Guess what, I noticed how warm it was getting while connecting to my work computer for 30 minutes. The CPU was 87% and I am using the most current release from the download site on Safari 6.0.2. The battery was literally draining 1% per minute or less you can watch the percantage count down like seconds obviously because the high CPU usage. The amaing Remote Desktop client I have running in comparison to a terminal server used a whole 1% cpu. This is a Pro2 license I am paying for here this should be a superior product to native RDP access. Looks like I will have to cancel some of my licenses since LogMeIn doesn't care about its customers. This has been ongoing since well over last year now and looks like no solution has been provided.