Bradley Hindman
Explorer
Now, there is the practical issue of time. If you're spending half the session with the warlock player doing a one man show basically investigating the entire adventure, then sure, that's no fun for anyone. D&D isn't a spectator sport. But, the solution here isn't necessarily to nerf the warlock, but, rather to adapt and overcome.
You know that the Warlock player is going to do this, so, prepare for it. Write up a handout beforehand for what the quasit learns. Ok, here's a map of where the quasit went (show an edited map of your adventure, leaving off stuff that the quasit couldn't have learned - traps, secret doors, etc. Heck, use that map as your handout. Freehand the map - it doesn't have to be perfectly accurate, it's not like the quasit is pacing off rooms. Label the map with what the quasit saw inside - this is a guard room with 4 orcs, this is common room, this is a garbage room, etc. Did the quasit overhear stuff? Well, does the caster speak that language? It's not like languages are that common - lots of critters speak stuff that the caster doesn't, in all likelihood. So, maybe the warlock learns half a dozen things - PLOT HOOKS FTW!
This is great advice. I had a long post prepared, but Hussar said it better. So, I will just post my main point.
While I do not know the players that are described in the original post, it sounds to me that the primary problem is the hogging of screen time by the warlock (leading to boredom in the other players). The DM should ask himself, why the warlock player does this. Does he/she really send out the quasit to gain information or does the warlock player do it to be the center of attention. The response to both motivations (most of the time) should be a quick "The quasit is successful" followed by a succinct description of what the quasit learned. Just narrate the result and move on.