After making my initial post to this thread, I reinstalled my XP Home SP3 op system and those tabs were working correctly afterwards (yesterday) with Firefox 3.6.18. So thought I had fixed it, but strangely the same problem has returned today. :'( I'm baffled by that observation, except that I've subsequently reinstalled various other application software so something might be incompatible. It doesn't work correctly with Internet Explorer 6 either on that computer.
DarkMaster's suggestion to press the Ctrl-R keyboard keys after left-clicking the tab works with both Firefox and IE6, as does my former suggestion to rightclick and open in a new tab or window. FWIW, that XP Home SP3 computer uses free avast antivirus as shown in my signature, and disabling the avast antivirus software temporarily has no affect. I want to try again (when I can find the time) after uninstalling the scripts shield, and disabling the sandbox, which have caused me various other problems in the past. Contrary to my signature below, I currently have those modules/features installed and active.
I also tried again with another computer which uses Windows XP Pro with Firefox 3.6.10, Chrome 12.0.742.122, Safari 5.0.2, and Internet Explorer 8.0.6001.187002IC. They all work OK. This computer runs the free avira antivirus software rather than avast, and is very different in the other installed software applications. It's a borrowed computer, not mine.
So in my limited testing, this bug appears *not* to be browser related. It is specific to a particular computer, and believe it could either be hardware or software related. I also wonder if there's any chance that the server software used to render the avast website has some prejudices built-in, so that it likes certain hardware or software better than others.