In one Law & Order game you're given a short tutorial on lawyering and tasked with interrupting the defense/prosecution (can't remember the details) whenever necessary. You also need to provide a reason for the objection (hearsay, argumentative, battering). It was very challenging because you had to pay close attention to everything they said and had a very short time to react.
Another thing I'd like to see is a protagonist who has some kind of limitation or disability like ADHD or autism. It should affect how they communicate and perceive the world. You could e.g. wake up to the alarm on a Friday morning, go to work as usual only to find that you're early, late, at the wrong office or it's actually Saturday and you don't work on Saturdays. You could have a conversation with someone who says one thing but means another, and it's not obvious what they want or why they're upset. Or say something that comes out wrong. If it has to be based on a profession (detectives are to adventure games what zombies are to... well, everything), the protagonist would have to be high-functioning enough to hold down a job.
A linguistics professor once said that reading emails from her dyslexic colleague is like solving riddles. Adventure games need riddles, right?
I like hidden object games because of the casual puzzles. Dominoes, sliding tiles, jigsaw puzzles... Can't really think of a way they could be naturally incorporated into a game though.
I'd like to see puzzles based on real-life situations. Again, the only situation I can think of right now is when my nephew's toy train derailed. "Oops! Bork. Bork." It wasn't much of a challenge to reattach the train cars and put them back on the track. But if I thought about it some more, I'm sure something would pop up.