[shiggerino]

Is he a drug addict, an imbecile, or is it just a speech impediment?

[stinkytaco]

As already pointed out, he was a drug user ("I like the Fed-Ex guy because he's a drug dealer and he don't even know it").

But the delivery is his style. Whether it's natural or not I don't know, but it certainly was an integral part of his comedy, similar to the monotone of Steven Wright (whom Mitch Hedberg is the spiritual successor to, in my opinion).

EDIT: Curiously, Hedberg suffered from terrible stage fright. I find him funny to listen to, but almost uncomfortable to watch because he would often stare at the stage or close his eyes.

[bbctol]

He had pretty extreme stage fright, hence the sunglasses and staring downward. By all accounts, just a very shy guy with a knack for clever jokes.

[freshyill]

That's not very nice.

[handedness]

He was a self-professed drug addict, but his speech was, as far as I know, an affect.