The NA creators had (perhaps only semi-seriously?) discussed regenerating the Seventh Doctor into a Doctor "played" by David Troughton, the son of Patrick Troughton. The BBC did not allow them to do it.
Also played with in the final Doctor Who New Adventure, The Dying Days, at the time of which a rumor went around to the effect that Virgin were going to spite the BBC by killing the Doctor off. It features quite a bit of foreshadowing to that effect, starting, obviously, with the title. The Doctor is apparently killed halfway through, but it's a Never Found the Body situation and he shows up alive and well in the climax, just in time to save the day.
Dawson Casting: Played with as at least one writer in the early novels described Ace (around 18 when the TV series concluded and played by Sophie Aldred, an actress in her late twenties) as in her twenties. This might indicate that a couple of years have passed since the first NA (though apparently haven't) or could explain why Aldred did not exactly look like a teenager.
The 50th New Adventure, Happy Endings, marked the occasion with Benny's wedding, with characters from most of the previous books turning up, plus a chapter featuring contributions from almost every author in the range up to that point, apart from Jim Mortimore.
The New Adventures also celebrated the 30th anniversary of the TV series with a five-part story arc, published in late 1993 and early 1994, in which the Doctor faced a series of old enemies.
Promoted Fanboy: The editors of the series made a point of being accessible to first-time authors—going so far as to recruit them from fanzines and the like—which led to quite a few of the novels being written by fans. Some names you might recognise: Paul Cornell, Mark Gatiss, Russell T Davies...
Name's the Same: Sort of. Both the Seventh and Eighth Doctors encounter a type 102 TARDIS in their run. However, the two couldn't be more different; one is an advanced but otherwise mundane TARDIS from Gallifrey's future. The other was not only once human, but the prototype basis for future sapient TARDISes.
What Could Have Been: Virgin at one stage, until the BBC rejected the idea, considered having the Seventh Doctor regenerate into an Eighth incarnation, who on cover illustrations would have been visually based on David Troughton, son of Patrick Troughton.