Okay, rewatch complete.
I do think that anyone who genuinely believes that something like "Space Babies" (which, to be clear, I did not particularly enjoy) was somehow out of line needs to pop back to 2025 and really look at what RTD was doing in his original run. A garbage bin belching after eating Mickey The Idiot kind of says it all.
This episode does a very, very good job of introducing the Doctor, and the basics of what he's all about (no Time Lords or Gallifrey to be mentioned just yet) to a new audience. Rose really was the best idea RTD had, allowing her to serve as the audience proxy moving forward. The focus on Rose's "domestics" was also a very good move, one not really replicated in the following seasons (though RTD certainly tried, and came pretty close with Donna's family).
The Nestene are a bizarre villain to open with - it's like RTD has a thing for smacking new viewers in the face with the goofiest things he can think of, just to set the expectations. Armies of department store mannequins in the streets of London are truly a sight to behold.
The episode isn't shot particularly dynamically, but it gets the job done.
One thing that I absolutely hate is Murray Gold's scoring for this era. The opening music over the montage of Rose's daily routine encapsulates it nicely - that driving percussion over the orchestral stuff just doesn't work for me at all. I'm going to try not to harp on it through the Tennant era, but I think Gold's work improves a lot once Matt Smith takes over. "The Doctor's Theme" is fantastic, though.
I actually think this one is a fun way of playing with that established dialogue in an unexpected way. The actual exchange goes like this:
It's entirely possible that "when he was promoted to Fleet Captain" and "I took over the Enterprise from him" are two separate events. And if that's the case, then you might as well sprinkle in some additional meetings in between. I don't think it's the original intent of the scene in "The Menagerie", but it's a valid alternative interpretation.
The Gorn thing is admittedly a bit tougher to explain, but I think it's mostly a Kirk problem - Spock doesn't really say anything to indicate whether the Gorn are familiar to him or not. And I don't think Kirk has me the Gorn (yet) in SNW?