The front tires on the military vehicle in the opening scene clearly show different tire treads from one scene to the next.
The AK used to tip the Jaffa's hat to reveal his forehead has a Chinese sling on it, which would not be found on a gun used by a Russian.
When Major Carter is attempting to cut her restraints with a scalpel, she is actually cutting the excess strap at the end of the restraint and not the binding portion of the strap.
This is incorrect. The trailer (on IMDb) shows clearly that she is bound by two layers or turns of the leather restraint and that she is cutting through both. The free ("excess") end is not cut at all.
Colonel O'Neill's Ford pickup has a decal on it indicating that it has a 5.7 liter Powerstroke V8 diesel engine. Yet the pickup clearly has the sound of a gas engine.
The army truck used by the Russians in the opening scene is an M.A.N. 630 German army truck. It was built in (West) Germany and Belgium for the German and Belgian army. By the end of the 70s, the German army had phased them out. It is very unlikely the Russian army would use this old and foreign truck.