Fridge Brilliance: Although nobody ever actually follows up when they say "I'll explain later", circumstances usually lead to the answer. For instance, Emma asks the Doctor why the Daleks didn't kill them, why there's a chair prepared, and how Zektronic energy will allow them to take over the universe in a matter of minutes.
The answer for the first one and the second are that the Daleks need the Doctor there to help in case something goes wrong, which it does. Their justification for keeping him alive and compliant is quite sound.
Zektronic energy allows the Daleks to kill the Doctor and the Master in such a way that they can't regenerate or resurrect. Since the Doctor is their biggest obstacle, they have a lot of investment in this ability, which would allow them to steamroll Gallifrey and change the timeline so that they're unopposed.
The canonical Tenth Doctor also likes to lick things. He can also be easily described by his fans as "Cute, sexy and lick-the-mirror handsome".
Richard E. Grant would later go on to play the re-imagined Great Intelligence in Series 7, who functions as an Evil Counterpart to The Doctor.
Twelve tells the Master and his companion to keep an eye on the universe, "I've put a lot of work into it." Moffat later put that exact same line into the prologue of Series 9, spoken by the actual Twelfth Doctor.
"The Doctor's Wife" confirms that regeneration gender-bending is possible. While the Doctor hasn't had one yet like in this parody, "Dark Water" reveals the Master has regenerated into a Time Lady. Her attraction to the Doctor has also escalated.
The new series even has farting aliens, albeit not as their primary method of communication.
in an episode of The Thin Blue Line (a sitcom starring Rowan Atkinson) while dealing with a lunatic falsely claiming to be a terrorist Rowan's character defuses the situation while stating "he is no more a terrorist then I am Joanna Lumley" and well that goes without saying.
Retroactive Recognition: The Tenth Doctor (Richard E. Grant) goes on to be the Doctor again for Scream of the Shalka (albeit as the Ninth), and was also in The Name of the Doctor, where his character threw himself into the Doctor's time line.
They Wasted a Perfectly Good Character: Not that it's really this story's fault, given it was a non-canonical charity special, but Richard E. Grant's brief-but-memorable performance here still makes more than a few fans annoyed that he never got the chance to play an official incarnation of the Doctor (Scream of the Shalka aside).