This is a "Wild Mass Guess" entry, where we pull out all the sanity stops on theorizing. The regular entry on this topic is elsewhere. Please see this programme note.
Doctor Whooves Adventures
Pinkie Pie is actually River Song
If only because everyone seems to think so, however it actually does make sense if you think about it...
She knew about the Weeping Pegasi and didn't read the letter the Doctor left for Twilight and Spike warning them about it, implying foreknowledge or experience with them. (Number 12 Part 1)
She knew about the mechanics of how the TARDIS was bigger on the inside. (Number 12 part 1)
She used weapons (a Battleax to be exact) and destroyed a Weeping Pegasus. (Number 12 part 2)
She can get in the TARDIS whenever she wants, to the point where she throws frequent parties. (Q&A 1-2)
In fact the only thing that goes against this theory is the fact that she didn't know how to drive the TARDIS as well as River can/better than the Doctor (Although she might be able to pilot it better simply because she is a pony and knows how to use her hooves but…) But he allows her to drive the TARDIS with him, showing she at least knows something; he doesn't let just anyone drive his TARDIS.
In the Chords of Chaos post-interview, someone asked if Pinkie Pie was River Song and even if they were joking when they said it was canon (perhaps…) the possibility seems to exist.
The show takes place in its own universe, not the main MLP universe
When the Doctor tells Twilight about Time Travel, she says that it's impossible. But there was a whole MLP episode about Twilight traveling through time, so she knows that it is possible. But that Twilight is not the same as this Twilight. They're parallel Twilights in parallel universes.
This would help explain whenever a voice in DWA doesn't exactly match their MLP counterpart...
Confirmed, DWA takes place in "The Boxiverse," which is parallel to the show. However, there are a few key differences, such as Daring Do (while still being real) actually taking place about sixty years before "Current day" MLP, minor elements to the plot, and more.
Derpy will become a future companion
She delivers key information about Night Shift's fate, the moment he needs it, perhaps too conveniently.
In the first mailbag, it's mentioned that she can always seem to find the a TARDIS even if it's to deliver junk mail.
During the season one trailer, she and the Assistant Doctor, can be clearly heard, meaning the Adventure Doctor will meet her at some point in the future.
There's an audition for someone named 'Herpy' on the Ponyinabox tumblr, this could perhaps mean that the Doctor is going to meet Derpy's father in a future episode.
Then again, who knows if Pony in a Box plans to follow the original tvtropes page? They might decide to shake things up.
Perhaps not entirely jossed, as Word of God in the comments for the new "Daring Do Adventures," Trailer from actual members of the Pia B cast state that while the TV Tropes page on Daring Do is used for inspiration, they are NOT using it as a "How To" guide for the series. It will be mostly original. So... the Jossed is possibly Jossed?
No. There have already been twoshorts showing that Herpy is a Daring Do character.
Word Of Sithking: No, we're not following the Tropes Page 1:1. That said, we will be using it as occasional inspiration.
They got married (Albeit jokingly) in the Express Delivery short, so at least the writers are aware of the fandom's pleas to see her in the Adventures.
There are more Timelords in Equestria
The Doctor seems unphased by the fact magic exists in the MLP-verse, meaning he, and thus the Timelords, may have been aware of this universe beforehand.
The walls of the universe are sealed, meaning that any Timelords outside the Doctor's home universe would have been safe from the Timelock.
The Master's laugh and a rhythm of four can be heard in the season one trailer, along with the line 'I am an old friend of the Doctor's'. Since a past human companion is unlikely this lends itself to the idea that it's Riversong or another Timelord.
The TARDIS works in the MLP-verse, evidence of a Gallifrey existing on some level in that universe.
On the other hand, the TARDIS works in the main Doctor Who universe, despite the destruction of Gallifrey after the Time War, so it's entirely possible that the Doctor (or other Time Lords, for that matter) could have modified the [TARDISes] to work without a Gallifrey. The Doctor could have also modified the TARDIS so that it could work in other universes after the near catastrophe in Rise of the Cybermen, and evidence of this could be possibly seen in The Doctor's Wife, where they exited the universe entirely with little to nothing in the way of negative consequences.
Goodnight will make a future appearance of great importance
She was created on another planet, meaning she may be slightly different from other fillies. What this difference is could be important to a later plotline.
In Good Day Goodnight, Goodnight is shown to be extremely intelligent (though otherwise still a child).
Her meeting with the Doctor lines up with Amy Pond's, meeting as a child. This could mean that there are plans for the future Goodnight to be a companion, or plot point.
On the Askviva Tumblr it's mentioned that Viva, a lunarpony from a tie-in comic (and later the episode "Shadows of the Lunar Republic), babysits her and knows the Doctor, meaning they are possibly still in contact.
Would the robot that created Goodnight give her up so easily? Her past may come back to haunt her.
The Doctor does not want to interfere in her life for some reason, and Twilight never seems to be with him when he interacts with her. The only reference to a companion in the shorts is that 'She is sick' during Goodnight Goodnight. The sick companion could be anyone...Perhaps even Goodnight herself.
The "Sick Companion," bit was actually a reference to Lauren Goodnight, the voice of Twilight Sparkle in-series, undergoing surgery on her eyes at the time.
Then again, it could easily be a reference to real-life events and some story element which has yet to be revealed.
In Cell Mates, a method of time travel is referred to as the "G9 Theory". If that has nothing to do with Goodnight (G8) then color me surprised.
There's a dark reason why Twilight hasn't told the rest of the main-six about the Doctor
She immediately lies to Rarity about him when they meet, even though the Doctor almost tells her himself.
In the fanfic material, even the future versions of the main six are unaware of the Doctor's true identity with the exception of Rarity, and she makes up a story for him the first time they meet Rainbow Dash and Applejack.
My theory is there's something stopping her from telling them. Something bad, perhaps to do with the Master.
…Or, she doesn't want them to think that she's crazy. "Hey guys, here's the stallion I'm hanging out with now. Oh, he's actually an alien with two hearts, and his magic blue box which is both a spaceship and a time machine."
But they fight weirder things all the time, the fact she hasn't told them is a bit strange.
Precisely: they fight weirder things all the time. Remember the reaction they had to Zecora? She was still from the same planet and had mostly the same biology. Doc's not even from the same universe.
In Wrong Way Backwards, the alternate-universe Doctor asks Twilight very pointedly: "Why haven't you told them?" We never get an answer, but it sure seems like something big is going on behind the scenes.
Vinyl Scratch Will be a Future Companion
In the the third Q&A she states that they've met before, and seemingly knows a lot about the TARDIS, implying she's traveled in it at least once. She seems unfazed by Fetch and the monster from the same episode, further implying she's seen stranger things.
The audio version of Octavia is voiced by Wollffeey, who voices Daring Do.
There is a version of Pinkie Pie in every timeline
Pinkie Pie's great-grandfather pops up to play a game of tag in Chords of Chaos. Even though Pinkie hasn't been born yet, the Pie name still pops up.
On the Tumblr there have been several posts about future characters, two, one named Coco Pie and the other Blackbird Pie, both look like Pinkie and share a last name. Coincidence?
Nope. Sithking Zero here, and just clarifying something: yes, Coco and Blackbird are related to Pinkie. Specifically, Coco is Pinkie's great-great aunt (and sister of Sergeant Pie, from the aforementioned Chords of Chaos), while Blackbird is Pinkie's granddaughter.
Pinkie Pie knows how the TARDIS works and was aware of the Weeping Angels to some degree, meaning that this could affect how she sees the world. Perhaps even giving her her fourth wall abilities. Because she's in every timeline, that means she's in every dimension, including perhaps one where they all live in a TV show.
Jossed... sort of. As stated before, Coco and Blackbird aren't "Other versions" of Pinkie, because they're both related to her. All of Pony In A Box's shows (unless otherwise mentioned, like the "Fallout Equestria" bits, "Storybook Projects," or other various non-canon bits) take place in the same universe, even if they might happen at different times.
Goodnight is actually a cyborg
How can she tell how many photons are being released from a star at a glance? Robot eyes.
She can do complex algorithms in her head, which could house an augmented brain.
She was created by a robot, so there's no guarantee she's totally organic.
Being only a few weeks old, everything she knows how to do must have been implanted if not into a totally equine brain than one that could be programmed.
The possibility of organic technology is certainly something that has come up before in Doctor Who, and she could be something like a human-model cylon.
The will-o'-wisps had outside help
In Pony of the Opera, the "auranvi" are revealed to be will-o'-wisps, creatures that create illusions and feed on anguish. This explains their attraction to Dorian Mode, and their means of manipulating him. But how did they create those audio-based mind-control devices? The Doctor specifically points out that this technology is way ahead of its time. The wisps aren't aliens or time-travelers, so it seems unlikely they had access to such tech. Certainly Dorian didn't invent anything; he's just a composer. So perhaps there was someone else, working behind the scenes, providing the wisps with this technology. (Alternatively, perahps the wisps just found this technology which had been left behind by someone else.)
Hm…little devices that go on your ears and suppress your free will? Sounds like the Cybermen…
Rarity will be a future companion
She designed the Doctor's suit, had the TARDIS crash into her living room, and has a huge crush on him.
In Traveler, the sequel fiction to Number 12, she actually is this in a future timeline.
If the Doctor ever reveals himself to the main six, I doubt they could keep her out.
Traveler will be a future storyline in the plays
There are small nods in several shorts. Bunsen and Delta pop up as foals in Goodnight's class, and Beaker, a minor rebel from the future appears in the short 'The Search'.
The story is unfinished, it could be waiting until the script is done to reveal the ending.
The short Cell Mates, takes place within the Traveler timeline, makes a reference to Raggedies, the Doctor's travels with Twilight going bad, and has the doctor say "What Time Is it!?" after crashing the TARDIS into a random place.
Confirmed: Traveller will be the first season finale.
The next villain will be a purple cat(Who may be involved in a Doctor Whooves crossover)
Based on this:  this cat has appeared on both the Doctor Whooves Adventures tumblr and the Doctor Whooves and Assistant Tumblr.
In the preview for Episode seven of Doctor Whooves and Assistant there is a large smile, and a dark voice says 'How can you find a proper place while not being proper yourself?". About an hour after that was posted an image of an invisible cat appeared on the Adventures Tumblr saying that exact same sentence.
On the Doctor Whooves and Assistant Tumblr, when asked what the name of episode seven they replied 'Wrong Way' and when a similar question appeared on the Adventures tumblr they replied Backwards. Recently the invisible cat popped up saying 'I guess I went the wrong way backwards."
The Doctor has been hinted to be regenerating in the next episode of both shows, could this regeneration have something to do with it?