Even Better Sequel: A child of LucasArts' golden age and it shows. Witty and ergonomic when compared to the original SCUMM game. DOTT is a very polished game which greatly benefited from the acquired experience of the designers, who averted several mistakes such as Unwinnable by Design. Maniac Mansion probably only bests it in one regard; multiple (and selectable) characters leading to multiple endings and adding Replay Value. The sequel is also Lighter and Softer, as it's less hardcore.
Hilarious in Hindsight: In the past there is a painting of Max in the 2nd floor hallway, and Hoagie describes him as a "patriotic dude". Fast forward to the Sam and Max reboot by Telltale Games, and Max becomes president of the United States.
Most Annoying Sound: "I don't wanna" / "I'd rather not" and their various alternates. Spoken whenever one of the characters attempts an action the game won't let them do, get used to hearing these voice clips a lot if you happen to get stuck and decide to just brute force your way through a puzzle by trying every item in your inventory on it.
"Where'm I gonna put it?" for Hoagie. One puzzle requires you to swap a squeaky mattress with another one. Unfortunately it is extremely picky.
Narm: The quality of the voice acting was pretty standard for an early nineties video game, but a lot of it really hasn't aged well. In particular, almost any time the characters are supposed to act surprised, it comes across as flat. Laverne sounds very spacey, but that was likely intentional.
Nightmare Fuel: Ed Edison is probably the creepiest character in the game.
There's also the IRS agents that come and abduct Dr. Fred in the middle of Bernard's campaign.
Scrappy Mechanic: Until Laverne gets the tentacle costume, she has to talk to a guard every time she wants to move between her cell, the yard, and the rest of the mansion. And if that wasn't irritating enough, you can only send inventory items to/from her when she's outside, (and this is almost the only reason why you'll ever be outside, as only two puzzles take place there). This leads to a lot of back-and-forthing between the yard and the rest of the mansion (stopping at the cell every single time in between) when you realise Laverne is holding an item someone else needs or vice versa.
Sequel Displacement: It's a sequel to Maniac Mansion, but a lot of gamers didn't even know since the game itself never states this, despite making numerous references to its predecessor. Fortunately, the original game is included as a game-in-a-game in the sequel (by "using" Ed's computer), though folks emulating today with ScummVM need to put in a little extra work to play it.
That One Puzzle: Use Squeaky Mattress with the other bed. You wouldn't think it would be this hard, but the game is very picky about what you are clicking and usually results in Hoagie saying "Where'm I gonna put it? Where'm I gonna put it?" even when you use the correct combination.
They Wasted a Perfectly Good Character: Laverine, Hoagie, and Bernard are merged into a three headed freak for the finale. However, the vast majority of the dialog from the protagonists in this whole section is only from Bernard while the others barely say anything, and a lot of it especially the examination dialog is simply reused from his section of the game. Just imagine the hilarity that could have resulted from the three describing what you're examining, wanting them to do, and so forth, not to mention all the contradicting and arguing with each other they could have done.
The Woobie: The future Edisons are a great representation of mankind. They are so sad and broken that the prospect of freedom is just a liability to them.