Cartoon Shading: No, that was just there to emulate the art style of the cartoon, plus money would have to be spent on adding this to the character models, which I think are fine as they are (though a little bit polygonal)
Map: When S&M came out, I didn't think a map was necessary, but after playing SBCG4AP, Sam and Max now feels really slow. Even in HtR I try to find the map icon instead of walking all the way back to the DeSoto. So that's a yes.
Icon-based dialog system: Only if the rubber ducky icon is in it.

One problem I found with the icon system is you don't know if there are more things for the character to say, which led to me getting stuck a few times. There's also jokes to be had in S&M and Monkey Island where your character doesn't want to say what you selected. (Like asking Bosco if the carpet matches the drapes in 205)
Trophies: Sure.
Collectibles: Yes, it adds a lot of replay value.
Costume items: Sure, Sam and Max and costumes go well together.

I always love the dress up game in HtR.
Mini-games: They were in it already, so yes.
Awesomeness rating: Again, replay value.
Preview: This might be hard to pull off, since all the clips have to be in the same location. In SBCG4AP you could get away with showing everything in the field because those green hills and plants are everywhere in Free Country, USA. But in Sam and Max it might be harder to pull off, unless it's like the 106 credits where all the locations are mashed together into one "set". Or pre-filmed as an FMV sequence.
Extended Play: Yes, but only if it's still possible to get all the collectibles and stuff in Extended Play. It's kinda annoying having to play the whole game again just to ask Marzipan the right question at the right time.