Factual error: In the classroom where Jack argues with Roger next to the chalkboard we can see a poster of the periodic table of the elements. We can see some elements that wouldn't be there in 1977 since they weren't discovered until 1999.
Continuity mistake: When Miles and Hurley deliver The Package, the way it's held is constantly changing.
Continuity mistake: When Miles is sent to deliver "The Package" (i.e. the dead body) to Dr. Chang, after the body is taken out of the van, Miles is seen closing the door to the back of the van. After a return from a flash forward and back to 1977, the door to the back of the van is open again.
Answer: He was eating a peice of an orange with the skin still on.
XIII