The Christmas Inversion (short story)

This story essentially takes place at the same time as The Christmas Invasion, with the Third Doctor arriving in Jackie's flat after the Tenth Doctor's TARDIS has been taken up to the Sycorax ship and leaving after his future self has been returned to London.
It's explained that the Tenth Doctor was able to complete his regeneration and stabilise his new incarnation by siphoning regenerative energy off of the Third Doctor, the latter referring to it as "energy osmosis".
The Doctor claims to have "never known a Rose". According to PROSE: Roses, his granddaughter was originally named Arkytior, "rose" in High Gallifreyan.

Continuity

Jackie mentions the Slitheen, the pig crashing into Big Ben, and Harriet Jones helping save the world. (TV: Aliens of London, World War Three)
The Doctor mentions the "Omega business". (TV: The Three Doctors)
Jackie believes that the Doctor has regenerated again, and, when meeting Jo and Yates, she thinks that Rose and Mickey have also changed their appearance. (TV: The Christmas Invasion)
UNIT's secret HQ is no longer located inside a building marked with a sign which reads "UNIT Headquarters," (TV: The Five Doctors) and is instead in a base under the Tower of London. (TV: The Power of Three)
Jackie recalls that Rose went back to "certain death" to save the Ninth Doctor. (TV: The Parting of the Ways)
Jackie recalls Rose telling her that she had met her father before his death. (TV: Father's Day, The Parting of the Ways)
When Mike Yates mentions UNIT's name as "United Nations Intelligence Taskforce", the Tower guard notes that its now "Unified Intelligence [Taskforce]." This same discrepancy was noted in a conversation between Jack Harkness and John Benton. (COMIC: Official Secrets)