Aluminum Christmas Trees: While being diagnosed as HIV+ is still a serious matter today, during the movie's late-1980's setting it was considered a death sentence. Mostly, because it was, as there weren't too many effective treatments for it at the time. It was also mistakenly considered to affect mostly gays.
Complete Monster: Carl Kenwood Jones, unfaithful husband to Mary and father to the titular Claireece "Precious" Jones, uses the two to fulfill his lust for sex and money. Carl molested Precious—since she was as young as 3 years old—and continued to rape her well into adolescence; verbally and physically abused Mary in the rare moments she objected; and showed no care to the grandchildren he fathered with Precious either.
The Woobie: Precious, obviously. Poor, poor, poor, Precious.
The 2009 film called Push has examples of:
Critical Dissonance: The film has a 23% in Rotten Tomatoes and is badly seen by fans who accuse it of being unoriginal, but IMDb has it with thrice that score and a lot of reviews which support its entertaining value.
The Bleeders just look plain silly when they scream. Even sillier when one scene shows them screaming...at a door. Except the one at the end, who was much more powerful than his two sons who had just been killed.
For Cantonese speakers, the fact that some of the actors (even those who are themselves Asian) clearly have trouble speaking the language and give rather stilted deliveries can be worth an unintentional chuckle or two.
They Copied It, So It Sucks!: As found by critics and audiences alike, the film's main flaw was its heavy borrowing of elements from media like Heroes, Scanners and even X-Men, which made it to be basically a Cliché Storm of the "regular people with powers" genre.