Awesome product, I'm so grateful it is offered for free.
I've just bumped into this ... bug last night. I have an XP machine that I am remote controlling using FF 4.0.1 (latest browser plugin) on a Mac running 10.6.7 however when FF 4.0.1 is open on the remote XP machine, its UI elements do not update. The content of the page updates sometimes but not all the time. Which means that if I go to yahoo.com in a tab, and then open google.com in another tab on the XP machine, I will not be able to switch between tabs using a mouse because I cannot see any changes taking effect. If I am lucky and the content is actually updating (outside of UI), I can blindly click on tabs and see the change reflected in the webpage rendering space but not FF UI.
I am guessing it has something to do with effects relying on GPU processing (like a 3d game) that do not get "caught" by Logmein's driver.
To make it easier, I have a screencast of the bug happening: