Can’t really compete with many of the above, but:
a few years ago I had a business trip to northern Sakhalin island in Russia (in the beforetimes when Russia was bad but not that bad).
Anyway, got the flight tickets, Visas, etc sorted out but needed one more bit of paper, the Border Guard Permit, to get up north. No problem, says CPY, we’ll have it waiting for you in Yuznho-Sakhalinsk, the local capital.
Duly arrived there, no permit.
Days two and three, still no permit.
Right, says CPY, we can’t have you hanging around here, get on the plane and we’ll hand you your permit when you land.
Now, bearing in mind you can go to jail for not having the right paperwork in Russia, that was a big fat no from me. Sure enough, the permit turned up the following day, but gee whizz what were they even thinking?