Some highlights to give a general idea of Moody's Magical Abilities:

Accio - Summons objects to hand
Alohomora - Unlocks locks
Aparecium - Reveals hidden things and people
Collovaria - Changes the colour of objects
Engorgio - Enlarges objects
Episkey - Heals minor to moderate injuries, up to broken bones
Expelliarmus - Disarms enemies by flinging the weapon away
Incarcerous - Binds up a target with ropes
Incendio - Sets an object on fire
Lumos - emits a beam of light from the wand
Petrificus Totalus - Causes one's body to become stiff and rigid
Protego - creates a magical barrier that repells minor to moderate attacks
Reducio - Shrinks objects
Reparo - repairs non-magical objects
Rictumsempra - tickling jinx
Stupefy - Stuns a target
Wingardium leviosa - levitates objects

[quote=@GreenGoat]
Also, does Moody know Crucio and Avada Kedavra? I feel like he would, considering what he is.
[/quote]

Technically yes, he would know the killing and torture curses. However, since these are both illegal to use on humans and carry a life sentence, a wizard cop won't be using them.