This is certainly a different story from other Bradbury stories, since it is set in the real world.  Even so, it still shares some themes with other stories of his.

I would say that a major theme is that of separation and death.  While no one dies, the two major characters (Mr. Ramirez and Mrs. O'Brian) are finding out that they will soon be dead to each other.  This makes them very sad.  Similarly, Mr. Ramirez is coming to terms with the idea that America is "dying" for him -- his dream of living in the US is dying.

To me, this is the major theme -- how people react to, deal with, and come to understand the changes that occur in their minds as they are separated from things they love.