Once you realize that this is a very loose retelling of Romeo and Juliet, a lot of the names fall into place:
Julie is Juliet
Perry is Paris
Nora is The Nurse
M/Marcus is Mercutio
And R is Romeo (much teased at, but never stated in the film)—who does, conveniently, "refuse his name" (as per Act 2, scene 2).
And the rather obvious balcony scene...
It makes sense that the zombies couldn't smell Julie in the airplane. Airplanes need to be airtight. No air means no smell.
At dinner with Grigio, Perry, and Julie, they aren't eating any meat. Meat is a luxury that has become normal, so obviously it'd be hard to come by during the apocalypse.
At the airport, R has a vision of the past and remembers how great it was when people were living and could enjoy each other's company. Ironically, his vision has everyone at the airport shuffling around like zombies, staring at their smart phones and not interacting with each other.
When Julie's group gets to the clinic/hospital in the beginning of the movie, it's mentioned they're looking for medicine - both to help the city, and to help the continuing search for a cure. Then R and his group show up... Well, they did find a cure!
"Whether they were your mother or your best friend, they are beyond your help," General Grigio warns Julie's group before they leave the camp near the start of the movie. The relationships he mentions make a lot of sense once you remember that Mrs. Grigio, Julie's mother and Mr Grigio's best friend, fell victim to the zombie plague sometime before the events of the book/movie.