Hi, I'm getting the same problem. I can't connect to Google because Google reports that the plugin has sent a malformed request; I can't enter the UA code manually either. I tried in both Firefox 5 and Chrome 12. I just upgraded to WP 3.2, and it is Version 4.1 of the plugin.
I just had a look at the plugin code. There is some show/hide scripting going on. The input element is set to display:none by default and clicking on the checkbox is supposed to show it, but it doesn't.
What I just did was use the web developer toolbar to disable inline CSS styles. That made the input box appear and I could enter my UA code.
I haven't tried to get the Advanced settings to show - it doesn't seem to be based on display:none so it needs another solution.
The UA code is so important I reckon the plugin should show the input box all the time and not hide it.