possibly that.... or....
I'm assuming you have a separate PHP log? Switch on Debugging up full. When it happens again, you should get a trace that will indicate what called it. I'm wondering if an out of date plugin is responsible.
You could also check that any optional plugins are compatible with 3.4!
I dug into this a bit as we have the same error in our logs. Check if it's always coming from the same IP. For ours it did and it's a link crawling bot that keeps trying to get the /calendar/set.php page for some reason.
The Apache transfer log will have info, for example:
216.244.66.241 - - [23/Aug/2018:01:12:28 -0400] "GET /calendar/set.php?return=L2NhbGVuZGFyL3123asucGhwP3ZpZXc9bW9udGgmdGltZT0xMTU0NDA0ODAwJmNvdXJzZT0x&var=showglobal HTTP/1.1" 404 4876 "-" "Mozilla/5.0 (compatible; DotBot/1.1; http://www.opensiteexplorer.org/dotbot, help@moz.com)"
Which leads to information about it at https://moz.com/researchtools/ose/dotbot
You can exclude certain pages or parts of the site using robots.txt