I consistently take a mental health day about every 3-4 weeks. It got to a point where I felt it was so predictable I had to go out of my way to make sure they at least didn't land on Mondays or Fridays every time. I'm not having it very easy at work right now though. Also, in my considerations, are that, with us being feds, all of the sick leave we accumulate will be worth exactly ZERO once we quit, whereas the annual leave will get paid out as a lump sum. Also, I wouldn't do it unless I already had substantial hours banked (I have 300 banked, roughly.)
It is really nice short term disability insurance though. The ideal is to save up 2080 hours. I knew a lady who got cancer and she took an entire year of sick leave. She came back to her job and she was essentially fine by the end of that year. Good stuff.
The thing about sick leave, as a fed, is that if you request it and it is for an approved purpose (medical exam, etc), your manager MUST grant it, they do not have the authority to not grant it. However, if abuse is suspected, they can start requiring a doctor's note every damn time. So that keeps me (relatively) on the straight and narrow.
One thing that I have been caught by though a couple times, is having a mental health day, and then within 2-4 days, actually get moderately sick (mild cold, hangover, etc) and then I have to pick myself up and go to work so as not to look too suspicious. That kind of sucks when that happens.