https://www.cvedetails.com/vulnerability-list/vendor_id-7971...
There are 11 total from 2015: one arbitrary access, one which allows administrators to run a process as root rather than the intended user (CVE-2017-1000082), and some DoS opportunities. Not great and several great examples of why C should not be used but hardly “every other month”.
Now, it's hard to compare that it against other systems because it combines functionality which people used to have to use third-party tools for or roll themselves so you have to count that against every buggy init script or supervisor feature, apps whose developers never got around to adding the hardening features which systemd does use, etc.