Anticlimax Boss: First Archivist in The Second Sky. Despite being the main antagonist, he's fought halfway through in a short and not especially difficult level.
Breather Level: The Second Sky has a few. "Chronometric Ruins" is deliberately toned down, as it introduces a potentially confusing new mechanic, the temporal split token. "Caught in an Eddy" gives the player a chance to recover after some extremely hard levels, and allows them to explore the other surface. "The Scorching Path" is a breather level... for no particular reason.
Journey to Rooted Hold's music is all excellent, but particular stand-outs are "Brood" and "Uncovered".
"The Architect's Oath", the title screen theme of Journey to Rooted Hold, with a stunning harpsichord instrumental section.
The Second Sky has a number of pieces by Emmett Plant that play during story segments. Particularly awesome tunes include "Within These Swingin' Halls" (Halph's theme), "Waltz Recombinant" (First Archivist's theme), "An Architect's Dream of Geometry" (the Farrow Child's theme) and "A Sympathetic Bartendry" (Tendry's theme).
Occasionally, there's a full on musical number. They are all awesome, except "Use the Fuse" which royally succeeded at Stylistic Suck.
Ear Worm: The title theme of Architect's Edition and King Dugan's Dungeon, "Whistler", which encapsulates the series' simultaneous silliness and epicness.
Goddamned Bats: Anything in the hands of a competent architect. Wraithwings typically get the most hatred, though, since they can fly, will run away from the player if alone (typically over pits) but in hordes, will swarm the player in a hard-to-predict fashion (since their movement is dependent upon the location of other wraithwings and the movement order of the whole horde).
Scrappy Mechanic: Percentage damage in DROD RPG. In holds that contain hot tiles or Aumtlich (which remove 5% and 50% of your HP, respectively), you have to keep your HP as low as possible to limit the damage. This means leaving potions untaken and, when you need to regain HP, running round to take exactly as much as necessary. This is not a big problem in the main Tendry's Tale hold — it contains only one Aumtlich, directly after a huge Flunky Boss battle that will leave you very low on HP anyway, so it's more a one-off trap for the unwary than anything else. But some usermade holds contain far more of these elements.
Stealth Pun: The Living Tar (literally, tar that is alive) might be one on a part of the phrase "Beat the living tar out of him."
Consensus says that Levels 8 and 13 of King Dugan's Dungeon definitely fall into this state, and there are also particularly nasty rooms spread throughout the series.
In Journey to Rooted Hold, it's Level 22, an exhausting run through several large horde rooms. Most of these don't require normal completion (i.e. killing all monsters in the same visit) but just getting through them so you can reach a different entrance and set off bombs. Yet somehow, just getting through these rooms is harder than completing rooms on other levels!
Some user-made holds are infamously difficult. Gigantic Jewel Lost comes to mind.
The official level set Beethro's Teacher consists entirely of Those Six Levels.
The Second Sky brings several. Shattered Mine, Temporal Anomaly, Experiment of Ages, Rapid Fortification, and Mother of All Roaches all fall under this category.
That One Puzzle: Each game has one or more rooms that have acquired particular infamy. This list uses DROD's usual coordinate system, e.g. "1E" means the room once east of the level entrance.
King Dugan's Dungeon: Eighth Level, 7S3E. Just mention "three tar mothers" to any DROD veteran and they'll instantly know which room you mean.
Journey to Rooted Hold: Sixteenth Level, 2S2E. A grid of obstacles interlaced with rock golems — enemies that leave piles of rock when you kill them. It's extremely difficult to avoid these clogging up the grid.
The City Beneath: Abyssian Fortress, 2S. Tarstuff clearing on a small platform, giving Beethro very limited mobility.
The Second Sky has quite a few. Shattered Mine 1E, Eye of the Storm 1E, WBCEND/Caber Testing Area 3S1E, Lemming Beach 2S4E, and Rapid Fortification 3S2E have all stumped many players.