These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
The Doctor and the Master have always had it, but the answering machine message takes the cake. Spoiler for slashiest moment in DW history follows:
The Doctor: (on recording) *giggle* — You have reached the good ship TARDIS. *giggle* We're rather — *giggle* — busy at the moment, *giggle* *giggle* so leave a message after the beep and we'll try to get back to you before you called. *giggle* — Stop that! *giggle* *giggle* The Master: We really should change that message.
The Master also complains about the Doctor's new (cute, female, of course) companion. The Doctor and the Master are basically married in this. The writer has said that although the Doctor's late former companion was supposed to have been the cause of his giggling, it could be the Master if you want it to be. That probably wasn't taken too seriously at the time, but now that the TV show has made this non-canon, there's nothing that says that can't be true for the offshoot continuity Shalka thus far stands alone in.
Nightmare Fuel: The Shalka. Between the sounds as they're stalking and the knowledge of what they can DO to you, these guys easily stand up to anything seen in the TV series in terms of how many nights you'll be kept up. This isn't something to watch alone at night, no matter how old you are or how Badass you think you are.
Specifically, Alison's description of how the Shalka forced her friend to torture herself to death with molten lava is one of the most horrific moments in any Doctor Who canon.