The woman who appears in the commercial for the Villain Awards looks suspiciously like supermodel Mindy Moleford, who ran away with the Mole King to the Mole Kingdom in season 1's "The Tick vs the Mole Men".
One of the dancers at the Villian Awards ceremony is wearing a costume of the moon with "CHA" (the first 3 letters of Chairface Chippendale's name from when he tried to carve his name on the moon in Season 1's "The Tick vs Chairface Chippendale") on it.
The Forehead: If you're so evil, eat this kitten.
The Tick: You know, Arthur, when Evil is afoot and you don't have any arms, you gotta use your head. And when Evil is ahead, and you're behind, you've gotta do the legwork! But, when you can't get a leg up, you gotta be hip! You gotta keep your chin up and kick some...
The Tick: When evil sees a twin headed Arthur-powered flying engine of justice barreling down upon it, great will be its trembling!
Evil Midnight Bomber What Bombs At Midnight: Ooh but I'm bad, baby! One of these days! Milkshake!! Boom!!!
The Enemy Awards: Obvious parody of the Emmy Awards.
Venus and Milo:
There is a famous statue called the Venus de Milo ("Venus of Milan" in Italian), which is missing the arms.