When the First Doctor, played by David Bradley, discovers the Twelfth Doctor, played by Peter Capaldi, he states that he thought he would regenerate into someone younger, at which point Capaldi insists "I AM younger!" While it is true that Capaldi is younger than Bradley, he is actually one year OLDER than William Hartnell was when he played the First Doctor in The Tenth Planet.
Although the First Doctor had softened considerably during his tenure, Steven Moffat nonetheless wanted to reflect the received wisdom that he was a crotchety, irascible old man. This would also provide an opportunity to poke fun at some of the more antiquated elements of his era, such as the condescending and chauvinistic attitudes that it sometimes adopted towards female characters, even though the Doctor himself had rarely exhibited these traits.
Although The Tenth Planet: Episode 4 (1966) and The Power of the Daleks: Episode One (1966), the episodes that originally included the first regeneration, are both among the series' missing episodes, the clip of the regeneration itself survives because it was used in Episode #17.17 (1973) of "Blue Peter."
When the 12th Doctor retrieves brandy from his cabinet, the bottle towards the rear of the cabinet reads 'Aldebaren'. River Song retrieves a bottle of Aldebaren brandy from one of the TARDIS' roundels in The Husbands of River Song (2015).
Rachel Talalay had actually shot a number of scenes from "The Tenth Planet", with a complete set reconstruction, recast characters, and the season ten Mondasian Cybermen. She said in an interview that she tried to make both the set, and the cinematography, as accurate to the original scenes, and original production values, as much as possible. She did admit to having fun with some parts of the set in particular, and embellishing with a "60s feel", and noted that some details of the action had to be invented. These scene recreations were not used in the final edit; the original footage was used in its place. However, these specially shot re-tellings were shown in the cinema release.