Did this also happen version 38.1.0?

If 38.1.0 is the version which immediately preceded 38.2.0, the answer is yes. I always run the latest version of Thunderbird but I don't pay much attention to version numbers. I've been hoping for a while that a newer version would fix the problem but it hasn't happened.

Are you using the default theme? If you use a third-party theme, does that help?

I was using the default theme.

I tried a couple of others but it didn't help.

Tools > Clear recent history brings the Preferences menus back to normal but as I click on different tabs (Display, Chat, Security, etc.) each time the menu is shorter until eventually only one line is displayed.

Thanks to Wayne Mery and finitarry for trying to help.

If you exit Thunderbird, move xulstore.json out of the profile to another location (such as the desktop), then restart Thunderbird, forcing it to recreate that file, does that fix the problem? It could be that xulstore.json got corrupted somehow. If that fixes the problem, you will have to redo any window size changes and toolbar configurations that you had done. If not, you can put the file back into the profile again.

Probably https://bugzilla.mozilla.org/show_bug.cgi?id=1185628 So try disabling hardware acceleration

finnetarry The only xulstore.json file I can find on my HD is in an Old Firefox Data folder, inside a k5drhudc.default folder on my desktop. Doesn't seem to exist in Thunderbird 38.2.0 nor in Firefox 40.0

Wayne Mery I went to Preferences > Advanced > General and saw that "Use hardware acceleration when available" had not been ticked.

Thanks both of you for staying with this problem.

--- I've never asked for help before on the Thunderbird Support Forum. Should I be clicking the "No" button? Seems kind of rude when you're both doing your best.

Marking "No" is fine, but not essential.

"Yes" and "Solves the problem" however are good to mark, when appropriate :)

I missed that you said safe mode failed, in which case acceleration should not be a factor - my bad. But it still could be a graphics bug.

I saw already such a report but can't find the bug.

Could you try to disable browser.preferences.animateFadeIn? To do this go to Preferences/Advanced/General and click on "Config Editor...". After confirming by pressing "I'll be careful, I promise". Now enter in filter field animateFadeIn. With double clicking you change from true to false. Now you can try again the prefs.

If this also doesn't work you can also try to switch mail.preferences.inContent to true like you switche the other pref. This would open the prefs in a tab instead a separate window.

I've found the origin of the problem (by turning add-ons off and then on one-by-one). The culprit is the Theme Font & Size Changer 38.3 (My old eyes can barely see the default interface.) However I used it for years without this problem. I'll contact the developers.

Don't know why the problem persisted in Safe Mode. I've uninstalled and reinstalled Thunderbird since then and the problem no longer persists in Safe Mode.

I seem to have bothered you three for nothing. Sorry about that.