10 Right at the start, as the Doctor steps out of the TARDIS and proclaims "Now that is HOT!" you can see his breath fogging, betraying the fact that it's quite the opposite!

20 The whole notion of the ship about to "crash into the sun" is riddled with holes. Most obviously, a sun is a great big ball of plasma & gas — it doesn't have a solid surface to "crash" into. Even if you're more forgiving and interpret that phrase to mean "pass through the sun's surface", that ignores the fact that the surface is actually the coolest part of the sun! Taking Earth's Sun as an example — the surface is "only" about 5,000 degrees — compared to the corona (roughly 1-2 million miles above the surface) which is between 1 million and 3 million degrees! So, assuming the sun in this episode is similar to Earth's Sun, in reality the "danger zone" for the ship would be at a comparatively distant 2 million miles away from the sun. Actually "hitting" the surface would be a piece of cake by comparison!
[Admittedly, sticking to the facts would make for a less dramatic episode, but I worry for the next generation of astronomers growing up watching this...]

30 Throughout the episode, as the ship gets closer and closer to the sun, it doesn't seem to make any difference inside the ship. Even when the heat shields are down to 5% it doesn't seem to, you know, melt anything. Nor is there a single sweat stain to be seen on anyone's clothing!
[Though maybe that's just ultra-powerful space age deodorants at work?]

40 Why oh why would any spaceship use a room inside the ship to vent heat into?? (Other than enabling the dramatic convenience of the TARDIS being "trapped", of course.) Concentrating the sun's heat from all over the outside of the ship into a tiny room inside the ship is a completely brainless notion — for one thing, they'd need pretty powerful insulation to protect the rest of the ship from the "concentrated" heat inside that room, and if they had such insulation, why wouldn't they cover the outside of the ship with it and remove the need for "venting" in the first place?

50 Considering their engines have failed and they're about to plunge to a fiery death, most of the crew seem to act as if they've all the time in the world! Witness the scene early on in the engine room, with the captain spending much of her time just standing around beside the Doctor, plus the crew members who couldn't be bothered trying to unlock the access doors to get to the auxiliary engines until the Doctor intervenes. (Did they have something better to do??) Then later on, just before she gets bumped off, Erina is moaning about having to do errands for Ashton. Get some perspective love, you're about to meet a fiery death in less than an hour, but all you can complain about are your chores!

60 There's no doubt that the "burning light" coming out of the infected people's eyes looks cool — but how can such a bright light be completely blocked by simply closing their eyes?
[Eyelids aren't 100% opaque... otherwise nobody would have invented the sleep mask!]

70 The Doctor's reference to "endothermic vapourisation", while it sounds convincing in the moment, is a meaningless tautology — all vapourisation is endothermic (i.e. it absorbs heat) — as opposed to exothermic (which gives off heat).

80 When the Doctor is looking at Korwin's bioscan result, the captain snatches it off him... but the Doc has it back in his hand an instant later.

90 Why do the infected put on those welding masks? (Apart from "because it looks badass"!) You might assume it's so they can keep their eyes open while they move around, without vapourising everything in sight — but before Korwin put his mask on originally (when he kills Abi), he can clearly can see where he's going with his eyes closed, so why not carry on without the mask?

100 In the keypad duel before the escape pod is ejected, the graphics on the control screen read 'Jettison Initiated', then 'Jettison Held', then 'Jettison Reactivated', but in the next shot it's jumped back to 'Jettison Initiated'.

110 When the escape pod actually gets jettisoned — talk about slow! Surely the point of an escape pod is to, you know, escape? Which usually means being ejected as fast as possible from the ship and whatever it is you're supposed to be escaping from... not drift off slowly into the sunset (in this case, literally).
[Though very fortunate for Martha and Riley, as the slow movement of the pod allows them to be rescued before they plunge into the sun. Not the first time that common sense takes a back seat to plot convenience...]

120 Also, earlier in the episode we see the ship spinning around as it tumbles towards the sun — but by the time the escape pod is ejected, it's clearly stopped spinning as the airlock stays facing directly towards the sun throughout the scene. But how does the ship stop spinning without any power in the engines?

130 When the Doc puts on his space suit to venture outside the ship and brave the solar winds, that looks like some pretty intense heat. Why didn't he do that half an hour earlier to get into the vent chamber and rescue the TARDIS? Could have saved everyone a lot of trouble if he'd just used the TARDIS to take the crew off the ship!

140 When the Doctor is being frozen in the stasis chamber, we can see from the display that the temperature drops to -50° and below, while all the time the Doctor is yelling in pain — but there's no sign of his breath fogging up in the supposedly freezing conditions!
[Which is unfortunate: some fog would have been just the thing to cover up the distracting sight of David Tennant's fillings!]

150 If dumping the fuel (i.e. releasing the living material captured from the sun) solves the problem, then why doesn't the solar intelligence direct the "infected" crew to just do that in the first place, instead of faffing around with "burning" the other crewmembers?

160 Even if you believe that a sun can be "alive" (and let's face it, we've heard far crazier notions on this show), you'd have to stop and ask yourself how one little spaceship could scoop up enough material from a sun to "hurt" it. Don't forget, a typical sun or star has a mass hundreds of thousands of times that of the Earth... so even if the ship grabbed up a planetary-sized scoop of solar material, that would be less than a fleabite from the sun's point of view!

170 At the end, why does the solar impact clock continue counting down after the ship starts to pull away and the computer is clearly saying "impact averted"?

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