Is searching a room actually interesting exploration? Really? After the fifteenth room in that adventure? I love exploration, but, actually make it exploration - finding unknown things and learning new stuff. Filling in that hex map, scouting ahead of the party, finding or making maps, discovering new information about the society that the PC's find themselves in - that's exploration.
Endless "I search the chest, I listen for traps at the door, I look for secret doors, Is the X trapped" is just as boring as endless meaningless combats or pointless NPC interactions.
I completely agree. If there's nothing of importance in the room, I straight up tell my players, and we move on. No rolls needed. If there's not a trap, then my players don't have to make a roll, because there is only one possible outcome. I try to move things along until they stumble upon something of interest.
When I design my dungeons (or any other explorable area), I try to also eliminate rooms that have nothing of importance in them. I'd rather have a small area filled with meaningful content, than a large space filled with a whole lot of nothing.
the player debates over what to do next, the 20 Questions to the DM, the endless worrying over gotchas, the quirky cagey NPCs, the asking to make checks instead of stating a goal and approach, the dilly-dallying on a combat turn, and so on. Get rid of that stuff and you save so much time that you don't have to cut out the exploration pillar and have the DM assume and establish what the PCs are doing.
My thoughts:
1 - "The player debates over what to do next"
I've never had a problem with players debating about what to do next. If it's an IC discussion between player-characters, I consider that gameplay, and my players are welcome to partake in it. If it is an OC discussion on what to do next, I try to give my players an occasional break to do this, when a serious situation calls for it (such as at the eve of a big battle). If it drags on too long though, I may break it up by having an npc move things along.
2 - "The 20 Questions to the DM"
I've completely eliminated these from my game, thanks to the great advice on these forums. For the most part, by listening a lot to Iserith's advice, and also Lanefan. By making it clear to my players that there are no gotchas, the players feel safer when exploring. I clearly telegraph threats, so they know when to be cautious and when they can feel safe. I also focus a lot more on getting the most important information across first: room size, doors, and imminent threats, -before going into details. The players know that if they want more information, all they need to do is investigate.
3 - "The endless worrying over gotchas"
My players have stopped doing this after I started following Isertih's example. Now that my campaigns no longer contain gotchas, and I clearly telegraph threats, my players feel more safe to trust my descriptions. When I say a place looks safe, it probably is. They no longer sleep in armor, with a knife under their pillow, or have someone stand watch in an inn. It's almost like getting rid of a trauma, haha.
4 - "The quirky cagey NPCs"
I've really changed up the way I play npc's. Nowadays I make it very clear to my players which npc's can be trusted, and which are possibly untrustworthy. I want to make sure that my players can feel safe in the knowledge that some npc's will never betray them, because it's simply not in line with their character. And some npc's are just straight up unlikable characters. I think it is important that the players can gauge the character and trustworthiness of an npc. Just like the plot of any superhero movie, there have to be trustworthy allies, and clear villains.
5 - "The asking to make checks instead of stating a goal and approach"
It is so difficult to get them to shake this habit. I have been trying very hard to get my players to stop doing this, and I have been some what successful. But then they play with another DM, and they are right back to doing it again. I find this a bit frustrating. I think this is because some of my players have been playing since 2nd edition, and so this style of play is deeply entrenched in their minds.
6 - "The dilly-dallying on a combat turn"
I don't think this ever was a problem for my players.