A make of alcoholic drink that comes in a variety of flavours, the most popular being either sour apple or butterscotch vanilla.
Customer (to barman): I'll take two shots of mickey finns sour apple and one of butterscotch.
A dose of knockout drops, such as chloral hydrate, a sedative/hypnotic, usually administered to some hapless barfly as a preamble to rolling him.
They slipped him a Mickey Finn, and when he woke up the next day, his wallet, wristwatch and jewelry were gone.
A dirty deed or a trick.
If you find drugs in your beer, you'd say "Damn! Someone slipped me a Mickey Finn!"