SummarySome clever ideas underlie the puzzles but the room is let down by tech issues and lack of maintenance. Made almost bearable by Nathan's GMing.
I'm going to address everything obliquely but you may consider some of this review to be spoilers. Proceed with caution. Especially when you get to the puzzles section.
ThemeThis could have been a good generic sci-fi "save the colony ship" theme. The Doctor Who elements are largely superfluous but generally done quite well. They do feel a bit scattered with pre-recorded announcements Jodie Whittaker combined with a Steven Moffat era prop and a Russell T Davies element. There's also a good bit of flavour on a collection of test tubes which name checks a lot of Doctor Who elements. Unsurprisingly there was a Dalek in the corner, which was nice, but not very interactive.
Set DressingA lovely, thematic design, but it needs maintenance. A panel was falling off the wall. Everything seemed a bit tatty.
Parallelisation This room is really bad about having multiple things to do. Most tasks need one or two people to achieve them, and most have enough space for a third person to offer advice but they are sometimes a spare wheel. Don't take four or more people into this room.
PuzzlesAll the puzzles were clever ideas let down by implementation problems.
"Find the pieces and put them into the spaces provided" was the only one that was more or less flawless, but also the least interesting.
"Insert the shapes into the slots with only an indirect view" was almost there, but made annoying by the shapes being quite similar.
"Match the objects to the outline diagrams and then select a subset of them using the rules given" suffered from the rules being pretty unclear and it being hard to match the objects to the diagrams. We ended up brute forcing the last half of this one.
"Select a subset of a different set of objects using yes/no questions" suffered a bit from the diagram of some shapes being unclear (this problem went away when we hit our first "yes" question and got a clear colour change). It also suffered from being dependant on a microphone link to the GM so sometimes there was a delay during which we weren't sure if we hadn't been heard or the GM was trying to work out the correct response. I can't think of a better way to implement that puzzle and it was a good idea.
"Arrange the things so something can flow from A to B" is a fairly standard puzzle. The only thing that made this hard was that it wasn't obvious where A and B where. The GM had to tell us!
"Connect the right things by touching magnets to two points" was, again, a brilliant concept, but the gloves with the magnets in were very tatty (I did not want to put them on and ended up just holding them around the magnets) and the sensors for the magnets were unreliable. We lost quite a bit of time hitting the right markers on the panel to no effect.
"Navigate the ship to safety" was another good idea, it was very on theme. The first flaw were that there was a barrier to getting started that we found very hard to locate, and when we did we lacked a physical skill that would make it easy to get over. We only managed that because of player knowledge of RTD era Doctor Who. The other flaw was that the map was a bit too busy and some spaces we needed to pass through were a bit ambiguous about actually being passable.
Finally, there was a "insert things into slots" puzzle that some things just didn't go into properly.
ConclusionThis room isn't worth your time. It's a nice design, but coming to the end of its life, and most of the difficulty comes from things not working properly.