The guys sing "O Canada", and include the line "From far and wide, O Canada", which wasn't even written until 1981.
When the guys are stopped at the border, a sign in the background lists the distances to several Canadian cities. On the sign, Winnipeg is misspelled as "Winnepeg".
There's a map of Canada in the RCMP office that shows Nunavut which only became a territory in 1999, not in the 1970s.
The Border Agents of any country do not monitor the people leaving it, rather they monitor the people entering the country. So it is wrong that the kids have to be inspected by the Mounties as they are about to leave Canada. Fez would've had a problem with US immigration, not the Canadian Mounties.
A Green Card is a document that allows a foreigner to reside legally in the US; it also allows you to enter the US, as it is a type of visa -- it has nothing to do with entering Canada, since it is a US government document for non-Americans. Fez wouldn't need his green card.
Fez is a foreign exchange student, so he has to be in the US on a student visa, not a green card.
The original plan to go to Canada without Kelso or Leo doesn't make any sense: As established in the episode earlier in the second season, "Halloween", Kelso is the only one of the kids who's over 18, and therefore is the only one old enough to buy beer in Canada. If they had gone without him, they wouldn't have been able to buy any beer in the first place.