Awesome Music: The whole soundtrack, really, done by the incomparable Jerry Goldsmith. Of particular note are the Creepy Circus Music from the carousel room (including the more disturbing variation later when it is played in counterpoint to the deep, loud, groaning sounds Hill House is known for), the music from the climax (starting from when Crain manifests out of his Spooky Painting), and the genuinely unsettling strings which play the main theme.
The giant, corpse-like statue of Hugh Crain trying to drown Dr. Marrow (in a fountain of blood, no less). He doesn't get a chance to explain what happened to him due to Nell screaming, and the event is never mentioned afterward.
Mary's moment with the harpischord, even geared as it may have been to remove the only possible psychic in the group (other than Nell) from the house, comes across as this too since other than one recording Marrow makes it's never mentioned again, and neither she nor Todd (the guy who takes her to the hospital) ever come back.
Nell's family who tries to employ her as a babysitter (and their weird child) are this to the ninth degree.
Esoteric Happy Ending: Hugh Crain is banished to Hell, the children's ghosts are freed to go to Heaven, and the haunting is presumably ended. (And Nell finally finds a place to belong, and peace.) But Luke dies, Nell dies, Mary got wounded (and possibly disfigured forever) and Marrow's experiment was ruined and never finished. The movie ends with Mr. Dudley's rhetorical question, "Did you find what you were looking for?" that Marrow can't answer...so was it all worth it?
Narm: A lot of the dialogue, particularly Marrow and Luke's awkward conversation in the hallway at midnight, his inane "I wonder what happened to him" in reference to Crain's statue, and much of Nell's dialogue during her final confrontation with Crain. Hugh Crain's ghost has been described as "the ghost of Cotton Mather" and looks like a giant Ringwraith while Owen Wilson manages to destroy any hope of tension the movie has and is ultimately decapitated by a lion's head flue that drops out of the fireplace. Also Eleanor is now a Messianic Archetype who defeats Crain with The Power of Love—Tropes Are Not Bad, but the presentation ...
Imagine Crain appearing on Grand Designs. "Right, over there I want a pool with a giant statue of me looking dead and a fountain of blood, over there I want a statue of an eagle, above the fireplace I want a lion head that drops out of the fireplace because it will be really funny and no-one will expect it and over there I want the Gates of Hell. Okay?" (Kevin McCloud looks slightly scared)
They Wasted a Perfectly Good Plot: Two of them! Both the "fake sleep study that is actually a fear study" (and the ethical nature thereof) and the investigation to discover the nature of the haunting and how to end it are intriguing plots...but combining them in one movie and not allowing either the full time to be developed causes both to suffer.
Unintentionally Unsympathetic: In the original Haunting, the doctor straight up tells the other three guests that they're studying the "ghosts" in Hill House. In this film, he's doing a study on group fear, but tells the others that they're only doing a sleep study. While deception is sometimes used in these cases, this change makes the doctor seem unnecessarily dishonest, even a little cruel.