I have neither palms nor dogs, but I wanted to share this anyway. I apologize if it is already common knowledge - I read about it at the blog of a lady who just lost her two dachshunds because of this: http://brightonandbear.blogspot.com/
Quoting:
Sago Palm (Cycas revoluta) and other Cycas species can also be potentially deadly to pets. These popular ornamental plants, native to subtropical climates such as the Southern United States, contain toxic compounds that Dr. Khan states “can potentially produce vomiting, diarrhea, depression, seizures and liver failure.” All parts of the plant are poisonous, but the seeds or "nuts" appear to contain the largest amount of toxins. As with the other plants on this list, very little plant material can produce a poisoning; the ingestion of just one or two seeds can result in very serious effects. An American Pit Bull Terrier in northern Florida became very ill and subsequently died from liver failure in March 2002 after chewing on the leaves and base of a Sago Palm in his owner’s yard.