dtgreene: Well, Rey is in the death machine, and she has the ability to manipulate people, so she could have gotten one of the stormtroopers to disable the shield.
PookaMustard: However, if we're gonna talk about her manipulating ability, let's not forget that she took her merry time to attempt it, as well as a failed attempt or two, so I can say it can be quite random to execute, and its not good when you're in unknown enemy territory that is constantly being watched over by other stormtroopers, although one wonders that if the First Order can make a planetary death machine like that then why didn't they put more effort into installing security cameras or, since its Star Wars, even sensors that tell if the person in question is on the side of the First Order or an intruder.
Also, consider that Ray has no prior knowledge about the plan to destroy the death machine to begin with. Saving her was part of the plan Leia put forth, but utilizing her was not.
I should note that there is a scene where Finn gets a stormtrooper to turn down the shield, albeit via different methods. Hence, I suspect that, had Finn not been there, Rey would have eventually done so.
Rey would have eventually run into Han Solo and learned of the plan to destroy the Death Star from him.
As a side note, even if they had the sensors, I have a feeling that Finn would be recognized as someone on the First Order's side, unless they were able to reprogram the sensors during that time.
GR00T: Saw the movie last night. Thought it was good entertainment and a quite good addition to the Star Wars movies. Hell, I liked it better than everything except Episode IV and V. Honestly, if you start to tear apart the plot points or dig too deep for logic in Star Wars material, especially the movies (any of them), it all falls apart pretty quickly.
The movie actually suffers from a few unrealistic aspects common to science fiction. For instance, if something is moving at the speed of light, you can't see it coming until it actually hits. (Basically, moving at the speed of light is visually indistinguishable from teleportation.) Also, in outer space, any sounds made by explosions or otherwise would not be transmitted through the vacuum, so from a physics standpoint, it doesn't make sense for there to be sound effects in space battles.
Another thing is, how does information travel across the galaxy so fast? (Remember, information only travels at the speed of light, no faster.)
As you said, it falls apart when over-analyzed.
One nice touch, however, is that, near the end of the movie, it gradually gets darker outside (which makes sense because of what's happening to that star).