After searching on Google Scholar, antimony (Sb) seems to be the main threat of leaching chemicals from the plastic, especially over periods of time and exposure to heat. Sb2O3 is used as the catalyst in the manufacture of polyethylene terephthalate and is probably carcinogenic but there is not good proof according to the WHO ("Although there is some evidence for the carcinogenicity of certain antimony compounds by inhalation, there are no data to indicate carcinogenicity by the oral route.")
Westerhoff et al. (2008) found antimony concentrations in nine brands of commercial bottled water ranged from 0.095 to 0.521 ppb, well below the US Environmental Protection Agency (USEPA) maximum contaminant level (MCL) for Sb of 6 ppb. The average concentration was 0.195+/-0.116 ppb at the beginning of the study and 0.226+/-0.160 ppb 3 months later, with no statistical differences; samples were stored at 22 degrees C. For exposure temperatures of 60, 65, 70, 75, 80, and 85 degrees C, the exposure durations necessary to exceed the 6 ppb MCL are 176, 38, 12, 4.7, 2.3, and 1.3 days, respectively.
Holy cow, does it get to be 140°F in our cars (that's 60°C)? If so, don't leave any bottles of water in there for 176 days. There are 3 or so of these bottles full of refill water in Tim's boat that I think he's planning to drink on his trip back to the mainland that have been stored since October 1. Temps on the island have probably been around 80°, so maybe it gets up to 100 in the hull of the boat... it's sort of in the shade and it's white, reflecting lots of heat.
But there is great variability in Sb release of these bottles depending on who made the bottle! A group of geochemists at the University of Heidelberg headed by William Shotyk (2006) reported antimony in 15 brands of bottled water from Canada and 48 from Europe. They found that waters from a commercial bottling plant in Germany had 0.008 ppb Sb before being bottled. That same brand, when purchased in the store in the PET bottles, had 0.359 ppb (2 orders of mangitude!). After an additional 3 months of storage, the same brand had 0.626 ppb. (I converted reported unit of ng/L assuming it's = 1 ppt.) In 14 brands of bottled water from Canada, Sb concentrations increased on average 19% during 6 months storage at room temperature, but 48 brands of water from 11 European countries increased on average 90% under identical conditions.
We don't know who made Tim's bottles that are sitting in the hull of cuba canoe so we can't guess how much antimony is in them.
Tangent: I'm really curious to find out if these 4 guys made their 11,000 mile voyage on a sailboat made of PET bottles. Their boat is called Plastiki! (Kon Tiki is a wonderful book, I love it.) Oops, just saw their webpage; looks like they are still glueing stuff onto the boat!