Firefox 3
At the April user group meeting, one of the attendees noted that the context menu does not always open using Firefox.
For Firefox version 2.x there should be no issues, but with Firefox version 3.x suppressing default context menus has been noted to be buggy (this is not TYPO3-specific, rather it's not working well for any application). The menu is available in other ways as a work-around.
Work-arounds
To "right-click" in the Pagetree, you should left-click the page icon rather than the page title to display the context menu.
In the RTE, all functionality can be achieved using the RTE buttons.
To edit cell properties, for example, left-click in the table cell and then left-click the cell properties button in the editor instead of right-clicking in a table cell and choosing cell properties.
Internet Explorer 8
Regarding IE8 and TYPO3, if you need to upgrade to IE8, TYPO3 mostly works with this browser. In fact, I am using it to author this news article.
So far I have noticed that the context menus are not available at all. Basic TYPO3 functionality (including creating pages/contents) works using the Page module and big buttons, but extended functionality (including Clear Branch Cache) are not available without the context menus and there is no work-around.
With any luck, fixes will be available next time TYPO3 is upgraded.