The scene with John Barrowman was originally written for Mark Gatiss. When Davison heard that John Barrowman was upset of not appearing in the 50th, Davison decided to shoot the scene with Barrowman instead.
The scene of David Tennant blocking the studio doors with a fire extinguisher was the first scene filmed for this story.
Tom Bakers absence and use of Shada footage is a reference to the Five Doctors thirty years prior where he declined to appear in the 20th Anniversary and they used footage from the unfinished story to allow him to appear, there's even reference to this in his answer-tone.
Tom Baker's absence from the plot not only references his refusal to appear in the 20th Anniversary, but also the fact that he was the only past Doctor to appear in the 50th Anniversary special (as the mysterious Curator).
Sarah Churm, who plays John Barrowman's wife, played Peter Davison's daughter in At Home with the Braithwaites (2000).