Hiding in a barrel as Snape earns you the "Solid Snape" achievement.
When you put together the skeleton in the hospital wing to make the Skele-Gro potion, the skeleton does the Napoleon Dynamite dance.
LEGO Harry Potter: Years 5-7
A skeleton dances almost exactly like Michael Jackson in "Burning Bridges".
Similarly, in at least two levels, you will get a couple of ghosts appearing and performing part of the Thriller dance.
After Bellatrix Lestrange jumps out of a cake at Bill and Fleur's wedding, you gain an achievement: "Cake or Death Eater?"
A level in which Kreacher the house-elf causes mischief is called "Kreacher Discomforts".
When Harry rounds up Dumbledore's Army at the Hog's Head, there's a puppet show involving Harry and Voldemort going on, possibly a shoutout to Potter Puppet Pals.