BBM trivia from IMDb:
Ang Lee struggled continually with the sheep during the shoot. Apparently sheep don't drink from running water, only ponds and dams. Ang tried all day to get the sheep to drink from a stream, but they wouldn't oblige. He had to give up on the shot.
Also, American sheep carry a bacteria/virus that Canadian sheep don't possess. The film's scene where two herds of sheep become mixed up had some nightmarish real-life parallels, as the Canadian government had expressly warned the filmmakers of dire consequences if they caused any disease to spread to the local animals from the south-of-the-border variety.