In an effort to determine the safety of feeding avocado to squirrels -- and what parts of the plant ARE safe for squirrels -- I've begun this thread. From a paper by Julia F. Morton, Perdue University Horticulture Dept; 1987 (highlights added by me):

Toxicity
Unripe avocados are said to be toxic. Two resins derived from the skin of the fruit are toxic to guinea pigs by subcutaneous and peritoneal injection. Dopamine has been found in the leaves. The leaf oil contains methyl chavicol. Not all varieties are equally toxic. Rabbits fed on leaves of 'Fuerte' and 'Nabal' died within 24 hours. Those fed on leaves of 'Mexicola' showed no adverse reactions. Ingestion of avocado leaves and/or bark has caused mastitis in cattle, horses, rabbits and goats. Large doses have been fatal to goats. Craigmill et al. at Davis, California, have confirmed deleterious effects on lactating goats which were allowed to graze on leaves of 'Anaheim' avocado an hour each day for 2 days. Milk was curdled and not milkable, the animals ground their teeth, necks were swollen and they coughed, but the animals would still accept the leaves on the 4th day of the experiment. By the 10th day, all but one goat were on the road to recovery. All abnormal signs had disappeared 20 days later. In another test, leaves of a Guatemalan variety were stored for 2 weeks in plastic bags and then given to 2 Nubian goats in addition to regular feed over a period of 2 days. Both suffered mastitis for 48 hours. Avocado leaves in a pool have killed the fish. Canaries have died from eating the ripe fruit. The seeds, ground and mixed with cheese or cornmeal, have been used to poison rodents. However, tests in Hawaii did not show any ill effect on a mouse even at the rate of 1/4 oz (7 g) per each 2.2 lbs (1 kg) of body weight, though the mouse refused to eat the dried, grated seed material until it was blended with cornmeal. Avocado seed extracts injected into guinea pigs have caused only a few days of hyperexcitability and anorexia. At Davis, mice given 10 to 14 g of half-and-half normal ration and either fresh or dried avocado seed died in 2 or 3 days, though one mouse given 4 times the dose of the others survived for 2 weeks.
The seed contains 13.6% tannin, 13.25% starch. Amino acids in the seed oil are reported as: capric acid, 0.6; myristic, 1.7; X, 13.5; palmitic, 23.4; X, 10.4; stearic, 8.7; oleic, 15.1; linoleic, 24.1; linolenic, 2.5%. The dried seed contains 1.33% of a yellow wax containing sterol and organic acid. The seed and the roots contain an antibiotic which prevents bacterial spoilage of food. It is the subject of two United States patents.
The bark contains 3.5% of an essential oil which has an anise odor and is made up largely of methyl chavicol with a little anethole.


According to this, it appears the leaves and seeds are the toxic parts to rodents, under these experimental conditions. For the entire article, go here: http://www.hort.purdue.edu/newcrop/morton/avocado_ars.html