Hi,
I have the same problem. IE7 and FF are fine. IE 8 (latest version/no updates available) does not display the profile, connections links on top of the individual profiles.
I also notice that IE 8 does not display the the images when using Nant's CB Profile Gallery and does not let me log out.
This is all happening on a Joomla 1.5.15 site with CB 1.2.1. The only other plugin being used is a UddeIM tab showing the user's private messages.
When I view an older site of mine built on Joomla 1.0.15/CB 1.1with IE8 I can see and use the profile, connections buttons and use them no problem.
R