Episode 2 is a standard science fiction plot with an Agatha Christie climax. All the important things happen on the sidelines.
The Doctor shows off the TARDIS by taking Rose far into the future to see the death of her planet. Odd choice for a first date, unless a person happens to already have wholesale death and destruction on their minds. Where did you just come from, Doctor?
The TARDIS is badly in need of it's 10 trillion year tune-up, and it appears that he's been jerry-rigging the controls. Sure the chameleon circuit and the pinpoint navigational control have been broken since the series began, but why is it running so rough? He was on good terms with the Council last we saw, he should be able to take it in for a tuneup.
The Expensive People have all come to watch on a posh movable observation platform. I hereby proclaim Lady Cassandra the ultimate winner of the anorexia contest. Yes, you can be too thin.
But what's this? The Doctor suddenly gets a whole lot less wooden around Jabe the tree lady. Could it be he's sexually attracted to powerful older women with a commanding presence? There weren't a lot of those in the original series. The Doctor was 792 when we first met him. This might explain his platonic relationships with most of his Companions. I can hear it now, "She's a fine girl, and she'd be a great lady in another 250 years. That's the problem with human women. By the time they're old enough to be interesting, they're dead."
Rose asks the Doctor personal questions. He's always been reluctant to answer those, but now he blows up completely. Why? Then he turns around and soups up Rose's cell-phone just so she can keep in touch with her family. Why does he value her connection to her people so much, and refuse completely to talk about his connection to his own people?
Jabe is aware of whatever war he fought in. Apparently all the Time Lords are believed to be dead. She's astonished to find him alive and offers her condolences over what happened. That makes him cry. What did happen?
Jabe's dead -- arrgh! A heroic death, but I wanted her to live. And the Doctor is a lot more willing to inflict pain and suffering on others. (Not death, though. Look at the blue cylinder.)
The Doctor tells Rose that his planet was destroyed in war and his people are all dead. That explains much about him and the TARDIS that is different.
"But where's the Eye of Rassilon?", my husband the continuity buff asks. "The TARDIS shouldn't work at all if that's gone. Wait a minute, didn't they hint in an earlier episode that they hid it on his TARDIS?"
"I thought it was in the Cloister well."
More special effects this time, but it was set in the future. The pacing at the end is a still rough, but a great improvement over the first episode. Still looks good.