The movie is "How to get ahead in advertising", from 1989. It's pretty out there, but the performances are superb, and I find it hilarious even 30+ years after I first saw it.
The Martini, well that is simple, gin and vermouth, with an olive or 4 thrown in. The gin is blue (the colour comes from Butterfly pea blossom that is added), as you can see here, but when it mixes there is a chemical reaction that makes it turn pink:
It's a great gin, and my favourite for Martini's. I've also used it in a G&T, but some of the more subtle flavours are lost with the tonic overpowering them...but the pink reaction is even more extreme.
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