Upgrade completed. Plugins seem to work fine and hook fire as well. Closing this for now. If we find any post-upgrade glitches new cases should be opened.

the error was caused by the emoticon plugin ( installed to test ) that tries to check preferences for anonymous users:

GET /accounts/self/emoticons~preference HTTP/1.1" 403 24

Deleted the plugin and this made the errors go away.

Staging upgraded to 2.13.8, feel free to test the new version.

The strange behavior that wasn't there before is a "session expired" warning when viewing patches without logging in. I had to press the "go anonymous" button 10 times to make it disappear - looks like some links that are accessed in the background now require auth.

When logged in everything seems to operate just fine.

Steps performed for the upgrade (as gerrit2 user):
wget https://gerrit-releases.storage.googleapis.com/gerrit-2.13.8.war
1) stop gerrit
/etc/init.d/gerrit stop
2) run upgrade wizard
java -jar gerrit-2.13.8.war init -d /home/gerrit2/review_site/

make sure to install the hooks plugin and upgrade existing ones. Skip installing singleusergroup plugin and Bitbucket auth. I also deleted all caches when asked.
3) reindex the DB
java -jar /home/gerrit2/review_site/bin/gerrit.war reindex -d /home/gerrit2/review_site/
This step is necessary (gerrit won't start without it) and took an hour during the last upgrade.
4) start gerrit
/etc/init.d/gerrit start

Best to sort out all the backup for the server before upgrading.

Seems like we have an issue which requires upgrading to 2.13.8:

Today we have seen this error again. Restart of Gerrit fixed this issue.
I have look a bit and found the following thread:
https://groups.google.com/forum/#!topic/repo-discuss/N5bIo4VlPGU

According to the above, there's a bug in Jgit. Its cache gets corrupted and it cannot find objects.
Restart of Gerrit causes it to clear the cache and that fixes the problem.

In order to fix that, you cannot only upgrade JGit (as it is built in inside Gerrit installation) but you have to upgrade Gerrit. According to Gerrit's release notes, this issue had been fixed only since Gerrit 2.13.7

It is not urgent but looks like a good idea to upgrade to this version or the latest (2.13.8).