The show's rules say that the biggest flag for demonic possession is sulfur. We often see Sam and Dean sniff for it, or sniff a yellow powder suspected to be sulfur. Pure sulfur actually doesn't have the rotten-egg odor we associate with it - that's hydrogen sulfide, which is a gas. Pure sulfur is odorless.
In every episode (through episode 2.20), the boys are showing off a Kansas license plate, the county tag reads "SG". In all actuality, the county for Lawrence should read "DG" for Douglas County.
In several episodes, the front of the Impala is visible and it has a front license plate from Kansas. Kansas does not issue front plates.
Despite never being shown carrying additional bags with clothing in their back seat and having no room in their vehicle's trunk due to their arsenal of weapons and demon-hunting paraphernalia, the Winchesters constantly have changes of clothing and even a selection of business suits for when they portray federal agents.
The Colt was stated to be made in the year 1835 by gun maker Samuel Colt who initially had 13 special cartridges. Cartridges didn't exist in 1835, back then the closest thing to cartridges were paper bullets, not the kind seen in the show.
In numerous shows it is clear that the Winchester's are not where they are claiming to be. The show is filmed in Vancouver, B.C. , Canada and it often appears that such diverse (and geographically flat) areas such as Iowa,Kansas and Indiana (as examples) are the rugged and mountainous areas of Southern British Columbia.
Sam Winchester frequently portrays a phony FBI agent to investigate cases. However, his hair is collar length and he's often shown to be unshaven. Both are unacceptable for FBI agents who are not on undercover assignments and Winchester never presents himself as being undercover.
In several episodes, characters mention the book of Revelations, from the Bible. However, it's just Revelation.