how can i repair the finish on a Brass bed?

Brass is only shiny immediately after it has been polished, then it starts to tarnish due to reacting with air.
The spots are probably just tarnishing where the protective lacquer has chipped or flaked and exposed the brass to air.
Clean and polish the tarnish spots with a non abrasive brass cleaner then cover with a clear lacquer or varnish, ensuring you overlap the existing lacquer.
Cover any new chips as soon as they happen.

Big Softy
January 2007