WARNING! THERE MAY BE UNMARKED SPOILERS!
Fridge LogicSee Headscratchers.
- Great, they saved the world and everyone's happy... except that now, the captain of the submarine has to try and explain to his superiors what happened to the six or so members of the crew who died, at least three of whom were ripped apart. What on earth is he going to say, that a 5,000 year old Martian killed them?
- Like was pointed out, for all we know other Soviets could have encountered aliens but it was hushed up. Given the state of Soviet politics, the military could well be keeping that knowledge from (all but the highest echelons of) the KGB and the Party.
- UNIT has a Russian branch, so presumably they stepped in and arranged for the cover-up just as the UK branch would've done if it'd happened to a British sub.
- The TARDIS's side-trek to the South Pole makes more sense if you consider that she'd remember having dropped by that same location just a few years later, Earth-time, in "The Tenth Planet", and will be heading back to the exact same time and place at the end of "The Doctor Falls". If there's any polar location she's got reliable coordinates for, it's there.
- The Doctor and Clara actually would have been stuck in 1983 for several months, unless UNIT had access to teleportation technology or the Doctor built one himself. Why? Because this episode takes place in the Arctic Ocean, meaning almost certainly north of the Arctic Circle, meaning that, since it's clearly daytime outside, it's summer in the Northern Hemisphere. Meaning that, conversely, it is winter in Antarctica, and full night at the South Pole. And it will remain night until October. These are conditions under which it is far too dangerous to fly a plane there for any reason other than a medical emergency. It wasn't until the late '90s that a flight to the Pole in winter even happened, and there was no landing (it was a supply drop in mid-July for the base doctor at Amundsen-Scott Station who'd been diagnosed with breast cancer). The first landing at the South Pole in winter took place in June 2016, for a medical evacuation. Now, UNIT does have access to greater technology than would be the norm in the early '80s. However, the South Pole is sufficiently isolated that any flight there in the part of the year where it's dangerous might draw attention. After all, "The Tenth Planet"'s Antarctic base is in a fuzzy area, since it was originally set Twenty Minutes In The Future, but in a future that didn't really happen.
- As an addition to the above, one wonders how the winter-over crew at Amundsen-Scott Station reacted to the arrival of the TARDIS. Even in the middle of a polar night, they likely would have noticed it, and possibly hauled it inside to get a better look at it, and wonder where the hell it came from. And then they had to sign confidentiality forms from UNIT several months later
"Was out photographing the aurora australis when I heard a strange noise. Followed it to discover a blue box sitting by the pole marker. Now half the base crew has come out to gawk, and we have decided to take it inside to have a better look at it..."