Paul/YMMV

Confirmation Bias: Ruth and her father's religious fundamentalism, so very much.
Fridge Brilliance: Why did Zoil stick with two clearly incompetent agents and give them as little information as possible? Because he was deliberately trying to sabotage the Big Guy's efforts to track down Paul.
Squick: Seeing Ruth's left eye for the first time.
- Graeme's bullet wound closing up.
- Clive mentions that the last time he had sex before meeting Paul was with a woman cosplaying as an Ewok.

"Clive likes boning space bears!"

- Our Man In Black makes his first appearance and, whilst looking serious and professional, performs the The Ketchup Test on a puddle of liquid on the ground... remember when Clive pissed himself when he passed out earlier?
Ugly Cute: Paul is basically a Grey with puppy dog eyes and a myraid of facial expressions due to his personality.
Visual Effects of Awesome: Paul himself, especially. He's so well-rendered it's easy to forget he's a special effect at all.
What Do You Mean It's Not for Kids?: Honestly, if you've been to the theater and seen this film, count the number of little kids you see. Clearly parents see the wide-eyed, cute looking alien in the commercials and, despite the R rating, feel it's totally cool to take the young'uns.
- There were even some cases in the UK where the trailers played before kids' movies.
Unfortunate Implications: Everyone the group runs into outside of a city is an ignorant redneck stereotype.
- "Everyone" meaning the Buggses and the redneck buddies, basically two independent instances. Not including the Karate Kid, Pat, Tara, a cop or two, etc...