Accidental Hero: Is quite an expert at this, as mentioned at the beginning of 2 as having killed his 1000th Drug Dealer (the latter two hit with his car, although they turned out to be drug dealers), and later on unwittingly hitting a police station robber with the door as he walks in.
The Ace: He seems to be something like this in the field of police work, although much of it happens through luck and several Accidental Hero moments.
The Comically Serious: His main character trait is that he's always deadpan serious despite all the bizareness that surrounds him. This is a key trait of Leslie Nielsen's acting style in his comedic roles.
Drives Like Crazy: Every time he's behind the wheel, he hits something. It's a Running Gag that he tends to crash into stuff outside the place he's driving to.
Hollywood Tone-Deaf: As discovered when he performs the National Anthem to an entire crowd of baseball spectators (that includes the Queen of England!).
Lethal Klutz: He accidentally killed his fiancée before the events of the first movie, a fact that Drebin remains blissfully unaware of.