although im not a rescue myself i do have a facebook page as I work part time as a fashion blogger for a major online retailer. Facebook is great at spreading information fast and getting it across to others interested in the topic you wish to promote.
I am a "fan" of a few local rscues who are on facebook too, they share new residents, their past rehoming sucesses come on to .be shown by their new owners etc. also its good for spreading the word on upcoming events at the rescue, and generally informing people what its all about.
one thing i do suggest is the use of competitions which really is popular on facebook- the prize doesnt need to cost, it could be to be the face of the webpage or something. people love this kind of thing!