If the log works in safe mode, and Conversations is your only add-on, then I recommend you disable Conversations and see if the log works in normal mode. I don't think the number of filters is a problem:

http://kb.mozillazine.org/Limits_(Thunderbird)#Message_filters

I disabled the conversations and restarted - no difference. A shot of the box that appears when I click on filter log is attached. I have checked the log box and clicked on ok, no change. I clicked on clear log and also got no change. This issue just started in the last week or so after I was testing and implementing a bunch of new rules and changes to others. I even downloaded and installed the latest version of the conversations add- on. I suspect a log file is corrupted, but do not know where such files might live or which ones to check. Any assistance would be greatly appreciated as this is a bit of a nuisance.

The filter log is filterlog.html, in the same folder as the msgFilterRules.dat file, in Mail/<popaccount> or ImapMail/<imapaccount>. To open the profile folder, Help/Troubleshooting, click Open Folder. Close TB before you delete or rename files.

As you can see from the safe mode kb article, safe mode involves a number of factors besides disabling add-ons, although I'm not sure which of these would affect the log. It's easy to rebuild the layout by checking 'Reset toolbars and controls' at the safe mode prompt, then 'Make changes and restart', but I would be surprised if this fixed the log issue.

I was able to restore the filter log functionality by following your directions and restarting in safe mode and checking 'Reset toolbars and controls'. Restarted the application and the functionality returned. Thanks for your help.