That bugged me a bit, but given the nature of the boat they maybe had limited options for alternate paths and perhaps figured they could get past it? Presumably not the first time it's happened if they've been there for while.
To be honest, I thought the 'Kane turning up the mindflayer on Dr Pershing' thing a few episodes back was more daft. Not sure if I missed something, but surely it would have been glaringly obvious that the reason Pershing had somehow been properly mindflayed instead of just 'refreshed' was that it got turned up to 11 and the obvious suspect would be the other ex-Imperial person left in the control room by herself?
On a different subject, I've been meaning to ask, I haven't watched any of the animated stuff, and I'm gathering I'm missing a fair bit of back story and references to it in this and the other live action shows. Not sure where to start with it though. I had a quick google and there seem to be a bunch of different answers. Any recommendations?
Yes, thought the same thing about the mind flayer. Anyone with half a brain would know she had done it to him and thus her cover is blown. Convenient Movie/TV thinking: if we don't see it, it didn't happen kind of thing. It was a bit of lazy writing, which definitely is an outlier for this series, but one almost expects it in the film genre.
Scorpius nailed it: Clone Wars and Rebels is "all" you need to watch to catch up. I say "all" because Clone Wars is seven seasons and Rebels is four (iirc). You'll understand basically all the references if you watch those.
However, in the last Mandalorian episode, they introduced some characters that come from Timothy Zahn's two trilogies about Thrawn (the Heir to the Empire trilogy and the Star Wars: Thrawn trilogy). I don't know how much reading those will be necessary, though, since the events in those books were declared "non-canonical" by the Disney hierarchy when they took over the Star Wars franchise. Perhaps some of the things in the Star Wars: Thrawn trilogy will take place on screen, but knowing about them beforehand won't really matter. I'm still hoping for a cinematic re-telling of the Heir to the Empire trilogy. They can change what's necessary to make it match "canon," but bring it on!