We see two things in this episode that are very rare for Doctor Who. 1) The doctor is scared for his life, and 2) The doctor does not mind wielding weapons for himself. What prompts these Doctor Who rarities? The Dalek, the Time Lords' arch enemies and adversaries in the Time War which wiped out both species save for the Doctor, and it appears, one lone Dalek. This was obviously an interesting episode as it had the mirror images of two lone survivors. Both feel alone in the world.
When the Doctor first recognizes the Dalek, we see true fear. The Dalek belts out its usual "TERMINATE" slogan, and the Doctor, realizing that he is locked in a room with the Dalek literally tries to claw the doors open, but only for a second. Once the Doctor realizes that the Dalek is powerless, his fear turns to immense anger, vitriol, hatred, and vengefulness. Like I said, it is rare to see such emotions from the Doctor. Sure he is often condescending to humanity's stupidity, penchant for violence, and lack of forethought, yet, here the Doctor seems all too human. The Dalek brings out what is usually hidden in the Doctor.
As we've seen in previous episodes, the Doctor's guilt (or possible guilt) over his past or future actions paralyzes the Doctor, and it is no different here. As the Dalek is regenerated (by Rose's DNA), the Doctor scrambles for a solution. He knows that this one single Dalek could wipe out humanity and that the only solution is to lock him 53 floors below the earth. Yet, the complicating factor is that Rose is stuck down there with him. In the end, his fear/anger toward the Dalek trumps all else and Rose and the Dalek are trapped. Yet, proving once again that the Doctor cannot think clearly when Rose or the Daleks are involved, he lets them out of the trap.
In comes the twist. The Dalek is changing. It is no longer the purely evil killing machine bent on destroying all things non-Dalek. It cannot kill Rose. Her DNA is causing the Dalek to mutate, to change.
The climactic scene comes as we have a face-off between the Doctor, now wielding an alien tech weapon bent on wiping out the last of the Daleks, Rose, caught in between, and the constantly evolving Dalek who is beginning to see the uselessness of his quest. The Dalek is evolving into a feeling creature, the Doctor is is devolving into a raging murderer, and Rose brokers the deal between them. In perhaps one of the more touching scenes of the series so far, the evolving Dalek asks Rose to order him to kill himself. The Dalek appears unable to act without orders, yet he seeks death as the only solution to his evolving with emotions. The Doctor wades through this scene with a flabbergasted look on his face. He can't believe what is happening before his eyes.
It is good to finally meet the Doctor's arch nemesis and realize that there are primarily two situations in which the Doctor is fairly useless: when he is confronting the Daleks and when he is fearing the loss of his companion. In those two situations, the Doctor cannot control his emotions, cannot think clearly, and appears to revert to just another "human" character, one as flawed as the next.