Anakin's "Not again," when his lightsaber is destroyed. Which becomes something of a Brick Joke later when someone apparently expected this to happen, as they brought him a spare.
The entire sequence where Yoda has the class of Padawans explain to Obi-Wan why information on Kamino is missing in the Archives. The tone of his voice obviously suggests that what he means is, "Figure it out, these kids can. Slowing you down, what is?"
Obi-Wan uses the Force to open what was earlier established to be an automatic door.
When Anakin and Padmé are being chained up next to Obi-Wan for public Roman-style execution, Obi-Wan gives Anakin a death glare and Anakin responds thusly:
Anakin: "Then we decided to come and rescue you." Obi-Wan: *beat* "Good job."
As Anakin and Padme have their first kiss at the lake house a soft version of their love theme plays. When Padme quickly breaks it off the music also cuts out! Also Anakin's face afterwards like he's thinking "What the hell?!"
In the documentary "From Puppets To Pixels" included on the special features, George describes Yoda as the "illegitimate child of Kermit The Frog and Miss Piggy."
C3PO gets his head separated from his main structure, and fused onto a battle droid's body:
"DIE, Jedi dogs! Oh... what did I say?"
Also from that scene:
"I'm programmed for etiquette, not destruction!"
And the battle droid's reaction:
During the Arena battle, Anakin and Padme take cover in an overturned chariot and engage in some Casual Danger Dialogue. Padme goes straight from delivering a Call Back one-liner, with a flirty look on her face, to having this horribly distressed look on her face as she goes back to shooting at the enemy.
Obi-Wan vs. Jango in the rain. Jango falls off the edge, and Obi-Wan gets an Oh Crap when he remembers that the two of them are essentially tied to each other.
Obi-Wan does the Jedi Mind Trick on a dealer trying to sell him death sticks.
Death stick guy: "You wanna buy some death sticks?"
Obi-Wan Kenobi (waves hand): "You don't want to sell me death sticks."
Death stick guy: "Uh, I don't wanna sell you death sticks."
Obi-Wan Kenobi (waves hand): "You want to go home and rethink your life."
Death stick guy: "I wanna go home and rethink my life."
Funny Background Event: as Padme is packing her clothes, two droids are shown putting in a brand new window in her bedroom.