Seriously hilarious! Probably the hardest/most laughs per minute of any game I've played. Only complaint would be as others have said where one needs to use evidence mid-dialogue. Perhaps you could make the UI element glow when its applicable? I know that would counteract the whole idea of puzzle-solving, but the puzzles take a back seat to the writing as it is, so I feel that it'd only be an improvement.
Regardless, kudos on the writing and story. Definitely one of the best out there!