When Jack kisses Rose and the Doctor goodbye, John Barrowman made a special effort to kiss both actors in exactly the same way... except on one take, when he kissed Billie Piper as usual, then said his line to Christopher Eccleston, started the kiss, and didn't stop until they fell on the floor. (Source: John Barrowman on the DVD commentary)
The street corner at which the TARDIS reappears after being sent back to 2005 is the same street corner where Rose's father was originally struck by a car and killed in the opening of Doctor Who: Father's Day (2005) prior to Rose altering the circumstances of his death.
Russell T. Davies wrote an alternative climax in which the Doctor and Rose actually head to the planet Barcelona, with Rose unknowingly on the verge of death due to her exposure to the time vortex. It was planned that this ending would still be recorded, at least partly to serve as a red herring. This ending has not been released to the public.
David Tennant's portion of the regeneration scene was actually filmed much later than Christopher Eccleston's, and without the presence of Billie Piper. Tennant's segment was recorded with him speaking to a piece of sticky tape indicating Piper's eyeline and then edited into the broadcast version.
Initially, the Controller survived into this episode to provide the Doctor with someone to talk to, until Russell T. Davies decided it would be more effective to have him converse with the Emperor Dalek instead.
The trivia item below may give away important plot points.
Series 1 contained an underlying story arc about the meaning and identity of Bad Wolf, with each episode containing several references to the name. In this episode, Rose sees dozens of Bad Wolf graffiti, which lead her to realizing that she is the Bad Wolf, and uses the words to always lead her back to The Doctor.