Not chmod related, but I've made some other interesting mistakes lately.
Was trying to speed up the boot process on my ancient laptop by changing the startup services. Somehow ended up with nologin never being unset, which means that regular users aren't allowed to log in; and since I hadn't set a root password, no one could log in!
Installed a different version of Python for a project, accidentally removed the wrong version of Python at the end of the day.
When I started the computer the next day, all sorts of interesting things were broken!