I'm running firefox 22.214.171.124 and do not experience problem 1 and 2 that you describe.
I'm not quite sure what your third issue is. In my surfing it felt intuitive and selecting a class on the bottom left pane did not modify the top left or bottom left.
Hmm ... I uninstalled and reinstalled Firefox and am still getting errors on Windows Vista. Also tried my XP machine with the following errors:
All from the primary Flex / AS link: http://help.adobe.com/en_US/FlashPlatform/reference/actionscript/3/package-summary.html,
1) If I select the first class in bottom-left-pane, the AAAARecord class, then the "Properties | Methods" links in the upper right disappear off the page on all 4 browsers*. I must stretch the window to 1350 pixels wide (across 2 monitors) before I can see these links. Only in one browser out of 6**, Firefox on XP, do they display correctly in a normal sized / full screen window.
2) Amazingly, in Vista / Firefox 3.6.13, after a reinstall, the first class listed is AbstractEvent, not AAAARecord. The first 4 classes are missing. If I go to the same link in Adobe Community Help -- i.e. search on ActionScript 3.0 Reference, and select the first result, now seeing the exact same URL as the one above -- the first class I see is Accessibility. The first 19 classes are missing, and classes are missing throughout the bottom-left-pane.
This does not happen in any other browser, but since I want to use Adobe Community Help, and Firefox is my main browser, it is problematic.
3) When I select the AAAARecord class (or the first class that does appear), the bottom-left-pane does change in all browsers / all machines, leaving the All Packages view, such that the bottom-left-pane now displays:
Package flash.net.dns classes
... (5 more).
From what I understood you wrote, you are not seeing this?
If this is indeed the intended operation, it makes scrolling through various classes nearly impossible. With the left-bottom-pane getting switched out constantly, one continually loses track when attempting to scroll through various classes.
* Vista Machine Browsers: Firefox, Chrome, and Opera (all latest versions, just installed), and Internet Explorer 7.
** XP Machine Browsers: FireFox latest version (3.6.13), and Internet Explorer 8.