Regarding the meteor shower referenced a couple minutes into the show, Niles states in Frasier's living room: "I was over here, having dinner with Maris. I will never forget that night." Then he indicates he was on the balcony witnessing the display ... and absolutely miserable. But two years previous, within a couple weeks, was the episode "The Seal Who Came to Dinner", where Niles tried to use Maris' beach house as a forum for his gourmet club, ending in disaster. Obviously he could not have been watching these meteor showers from two vantage points at the same time. Plus, at that time, Maris and he were separate and so it seems unlikely he would have had her for dinner at the Crane apartment.
Although it is in needed in order to add to the comedy value, in the previous episode "And the Dish Ran Away with the Spoon: Part 2", the fire door was not wedged open and was able to be used unlike in this episode.
Niles charges the fire door and it refuses to open. The point of the panic bar is so that the door can be opened out in case of fire. To have the door locked from the inside is a serious breach of fire code.
Ignoring the fact that Niles wasn't at Frasier's apartment for the last meteor shower a meteor shower can't be observed very well, or even at all, in a brightly lit city.
Not changing a pollen filter isn't going to break a car.
Daphne claims that she is unable to slide the key underneath the door so that they can leave the patio. However, Niles is on the free side of a fire door. He could just open the door using the panic handle.