Of a sort; Terrance Dicks' famous axiom that the key defining trait of the Doctor throughout his incarnations is that he is "neither cruel nor cowardly" becomes enshrined in canon as part of the promise that the Doctor's name represents.
The gag with the Doctor doing a Double Take when he spots an aged Fourth Doctor was, funnily enough, proposed by Tom Baker himself during his convention appearances. He approached the showrunners with this idea as early as 2007, while praising David Tennant's take on the role.
Acting for Two: With three different characters in the same scene, no less, thanks to Zygons impersonating them. Also happened before that, with a completely separate character as well!
According to Sylvester McCoy, no surviving pre-1989 Doctor was approached to reprise their role, which made them feel a bit thrown away. Though Tom Baker shows up in the episode, he wasn't playing the Fourth Doctor.
Averted with all of the previous Doctors being in The Five(ish) Doctors Reboot. Clearly a special project by the BBC and all of them having a great time. Although that was specifically planned and written by Peter Davison when he realized that The BBC weren't going to be contacting the previous Doctors to be involved in the real special.
At the same time, Christopher Eccleston, the first of the 2005-onward Doctors, was hard-pressed to come back, and fans wanted him to show up to the party essentially to complete the triad of revival era Doctors. However, he decided with some difficulty not to take the offer, with the mentality, "never bathe in the same river twice." This coming from somebody whose tenure was only one series long due to personal issues with the way things were run on the show during his time. But, Eccleston did not rule out a future return appearance and jokingly said he would happily come back for the 100th anniversary. As such, John Hurt was given what would have been his role.
Early Installment Weirdness: Peter Capaldi later revealed he was wearing a purple coat that served as a prototype to his Doctor's final Crombie coat costume. There are faint glimpses of it in the shot with his eyebrows.
As of Series 9, the Twelfth Doctor now has a red velvet coat that looks rather more similar to his getup in this episode, potentially allowing for his involvement in the saving of Gallifrey to occur during the time period of the latter half of Series 9.
Several of the War Doctor's lines match up with some of the complaints fans have with the new series, such as asking if there is going to be more kissing in the future and the several uses of the sonic screwdriver, as well as the use of Buffy Speak.
Tom Baker's line of "revisiting the old favourites" is a reference to the Fourth Doctor being the most popular one amongst older fans.
Take That: A stealth one, though probably unintentional. In the bonus video of Tennant and Smith, Tennant mentions that the pressures of playing The Doctor are still 89% wonderful. That would make the other bit, the negative parts, 11%. He's talking with Smith, of course, who plays the 11th Doctor.
Christopher Eccleston was approached about appearing in the special but turned it down after finding out that Joe Ahearne, a director he had enjoyed working with, wouldn't be able to helm the special. Still sneaks in with Stock Footage like everyone else, though.
Kate's line about the disastrous consequences of information about the Doctor getting into the wrong hands was supposed to be juxtaposed with a film poster for the Cushing movies, implying that they are fictional in-universe. Unfortunately, they were unable to afford the rights.
Channel 5 actually obtained the rights to broadcast the Cushing films in the UK and showed both of them during the anniversary weekend. This was welcome because they were careful not to clash with any of the official celebrations on the BBC, but still, if they been able to show the poster, the Channel 5 transmission would only have reinforced Kate's point!
In an interview, Steven Moffat remarked that while writing the script neither David Tennant nor Matt Smith were under contract to appear, and he hadn't been able to secure Chris Eccleston. The only contracted actor he actually had was Jenna Coleman. So, while the actor situation was being sorted out, he was forced to brainstorm a Doctor Who 50th anniversary special with none of the people who had ever played the Doctor. In his own words, his best idea for the "Absolutely-no-Doctors-in-it-at-all" anniversary special had fictional versions of the Doctor (played by different actors) appear in all sorts of different films, and Clara would have to piece together the mystery of why they all seem so familiar.