Normal skill checks
The standard DCs for skill checks, for example for discovering secret doors with Wisdom (Perception) or Intelligence (Investigation) is given on page 238 DMG under Typical DCs:
| Task | DC |
|---|---|
| Very easy | 5 |
| Easy | 10 |
| Moderate | 15 |
| Hard | 20 |
| Very hard | 25 |
| Nearly impossible | 30 |
This makes sense for normal characters. If they are proficient, even at mid levels they might have +9 in those skills, enough to make detecting hard to detect door close to a coin flip. Even at highest levels, they might have a stat bonus of +5 and a proficiency bonus of +6, for a total of +11, making it barely possible for legendary heroes using their strongest abilities to achive a nearly impossible task on a roll of 19 or 20, and having a shot somewhat better than fifty-fifty for a hard task. So you can just use what it says on the tin to set DCs for your secret doors and whatnot. Hard to discover secret door? DC 20.
Expertise breaking bounded accuracy
That changes with Expertise. For example, a rogue or any character with the Skill Expert feat in one of these skills would have +8 bonus from Expertise and by level 11 gets the Reliable Talent which sets proficient skill check rolls smaller than 10 to 10. Their minimal result is already 23. In practice it may be only 22, as they typically put their best ability score on Dexterity, but either way, they would discover all hard secret doors automatically. In tier four, they most of the time would discover even that nearly impossible secret door. (There are uncommon magic items like eyes of the eagle that could turn this into always, but by then you maybe have better things to do with your attunement slot).
Now, there are other ways to detect secret doors, with uncommon items like the wand of secrets, or with spells. But those are not always on.
Tomb of Horrors
Tomb of Horrors is an infamous adventure light on combat encounters, but heavy on traps and secret doors. In the original AD&D version, normal characters had a 1 in 6 chance (about 17%) and elves had a 2 in 6 chance (about 33%) to detect secret doors, and everyone had a 3 in 6 (50%) chance to detect pit traps -- when tapping for them with a pole. The 5e version of this says:
A character who succeeds on a DC 15 Wisdom (Perception) check discerns the edges of a pit's lid.
With DC 15 even normal skilled PCs with max stat have a 75% chance to detect these features. For a rogue of level 11, it is automatic detection. This DC clearly makes it much easier than it was in the original.
Now, if I want to replicate the original experience more closely for Tomb of Horrors, I can of course increase that DC to make it approximately as deadly as the original. But to what target number?
I don't want to adjust this on the fly in reaction to the party composition -- that just feels like cheating to negate the investment party members may have made into their characters' abilities.
What may be a challenge for a group without a rogue might be near automatic success for one with a rogue, and what might be challenging for one with a rogue might be near impossible for one without. I wonder how to deal with this? What number would you set the DC to as an adventure designer to create a challenging experience, given there is Expertise in the game, but you cannot know the party composition?