In the new Doctor Who how Rose is "in love" with the Doctor.
Girl, you. Are. A. TEENAGER. The guy is well over 1300 years old (though he says 900)...which for a Time Lord is a teenager...but regardless! And it's not totally an age thing! It's the fact that with 1300 years, she has no IDEA of what the Doctor has seen, done, experienced, etc. etc. With her being in the new era, he had just committed double genocide with one big KA-BOOM, one of which was of his own people and his planet!
So really, all her pining over him was just...urrrrgh...and the way she just DROPPED her boyfriend was irritating too, and every other time she saw him, she was ignorant of how she had hurt him doing that!
And on a more humorous notes, when his companions try to talk into the environment, like Martha trying to speak in Iambic pentameter to Shakespeare, or Donna (Donnaaaaa <3 ) trying to speak "posh" when going to a party with Agatha Christi. Fortunately, the Doctor was there to stop it for me =P.
Oh, and Evolution of the Daleks when Solomon was trying to talk the Daleks out of attacking the Central Park Hooverville. More on an "You idiot, stop it! They're not going to listen!" level, though.
Then again, Doctor Who has a facepalm moment in every episode, even the awesome ones.