When I print mailing labels, I always get a comma after the zip code and the zip is on a seperate line. What am I doing wrong?

You will need to edit the label template that you use and remove the comma command and remove the line break for the zip code.
There is an option in the editor to end a piece of data with a comma followed by a space. You might like to change this to just a space.

This is fairly straight forward - especially if you are using a standard label type like an avery sheet.
Hope this helps.