Out-of-Character Moment/Took a Level in Jerkass: In the episode, "Pulp Boot Camp," she acts very rude and disrespectful to her parents and Suga Mama. She also turns against her friends and bullies them along with the Gross Sisters. She eventually gets sent to Boot Camp and then realizes the errors of her ways when the Gross Sisters refuse to house her and tell her that the fact that she was sent to boot camp, she was a hardened thug instead of a regular bully.
Properly Paranoid: In the episode "Thelma and Luis," when she finds out that the retirement home that Papi stayed in was actually a prison. She was right all along, but the adults didn't believe her (except for Suga Mama). She was proven right at the end of the episode, though.
In another episode, Penny's teacher gives her report on Hillary Clinton a failing grade, despite the paper being excellent in quality. Penny concludes that her teacher has a personal grudge against her, which gets her a lecture from her mother about "making excuses"...which it turns out Penny actually wasn't, because Penny's teacher did give her an unfair grade, but not precisely because of a grudge against Penny. Actually, the teacher had a grudge against Suga Mama, which she took out on Penny.
Too Dumb to Live: He sometimes falls into this when he ignores advice given to him regarding his safety and ends up bringing some of the bad luck on himself and also going through near-death experiences.
Hypocrite/Moral Myopia: She openly jokes and talks about cheating on Oscar with other men and repeatedly flirts with men in front of Oscar, but gets angry when Oscar does the same thing with other women. An infamous example is in the episode "Ainít Nothing Like The Real Thingy Baby."
In one episode, he instead cries, twice. First, tears of joy when Suga Mama is marrying someone else, but she thinks he's sad. Second, he's sad when she's single again and back to her old self, and she thinks they're tears of joy.
Even Evil Has Standards: The Gross Sisters refuse to house Penny after she escapes from boot camp, figuring that while they're bullies, the fact that Penny was sent to boot camp makes her a hardened thug.