Only roll the dice to resolve an action once, and only if there is risk of failure.
This sounds like common sense, and it should be. However, if the last 10 years of roleplaying has taught me anything, this idea is seldom put into practice.
I remember a game in the recent past where the DM had us traveling through this tunnel. I can't tell you how many times he had me roll perception, but it was a lot. Granted, this DM was fairly new to the game, but I see this mistake repeated by veterans just as often.
Why is it a mistake? To start, it slows the game down and detracts from the primary reason you've assembled your friends around the gaming table: to have fun. The most important reason is that it trivializes success and increases the risk of failure.
Failure often has disastrous consequences (you don't see the spider hanging from the ceiling, you don't notice the tripwire that springs a trap) but success feels empty. It's often even worse when this back and forth between the players and the DM become bereft of any description.
Why not just have them make a single Perception check to resolve this scene? Or maybe two; one for noticing structural irregularities and another for spotting any wandering monsters? Allow them to re-roll once they've been on the receiving end of a trap or ambush, but make the new result stick, even if it is lower.
The worst examples of this kind of incremental success and disastrous failure I can think of are unopposed checks, like Climb or Acrobatics. Rolling 30 checks to scale a cliff face isn't exciting nor does it make me feel like my character is particularly good at climbing. Why can't one check suffice?
Of course, not all of the blame falls on the DM's shoulders. After failing a check, the first question most players ask is if they can retry. It's the kind of question you need to have a good answer for beyond, "because I said so." Most DMs allow this for things like climbing to be re-rolled. Why? Failing a check can mean much more than just saying, "You were not successful."
Perhaps the cliff face is wet and without the proper gear it will be too slick. No re-rolls until that gear is attained.
Maybe the character was able to ascend X feet but then fell and took damage based on their margin of failure. You could allow a re-roll, but the idea is that this will deter them without considering a different strategy.
Perhaps the path they took leads to a dead end and now they have to approach from another direction.
If re-rolling is always an option, then what's the risk? What's the point of casting the dice to begin with?