10.5. I have updated Enigmail on Thunderbird, and now it keeps telling me: “A previous install did not complete correctly. Finishing install.”

Follow these steps:
Go to your Thunderbird installation directory and delete the file xpicleanup.dat.
Run Thunderbird, go to Tools → Add-ons → Extensions, select the Enigmail extension and click on Disable. Restart Thunderbird.
Install the new version of Enigmail, then enable Enigmail again from the Add-ons Manager.
Restart Thunderbird and this problem should be fixed.