The Canadian flag shown in the ceremony near the end of the
film wasn't adopted until 1964. At the time depicted in the movie, Canada still used a "modified Union Jack" type of flag called the Red Ensign.
In the barroom brawl sequence beer signs are plainly visible on the walls...Some are neon, some are not, all are out of place for that era. Until the late 80's/early 90's Coors beer was only available in Colorado and select places west of there, not in Montana...Also, that particular neon sign was strictly 1960s and would have been totally out of place then as well. The Lucky Lager sign was likewise 1960's in design - even though the beer would have been available then.
All of the American officers, when wearing neckties are wearing Army Green neckties. They should be wearing khaki ties. Army Green did not come along until well after WW II. The enlisted men are all wearing the proper ties.
At the beginning of the film Captain Cardwell draws a handgun and shoots a rattlesnake, then twirls the pistol before holstering it. An experienced gun-hand would never twirl a double action revolver for fear of an accidental discharge. However, the double action pull weight is about 14 pounds so it could be spun without causing a discharge.
Although the crossed-arrows insignia worn in the film by the First Special Service Force were fact, the red berets were pure fiction. All members of the Force eventually wore U.S. Army dress uniforms with U.S. paratrooper boots and distinctive red,white, and blue braided shoulder loops, overseas cap piping, and parachute wing backings.
Although the Union Jack was the official flag of Canada prior to 1965, during World War II it was the Red Ensign that was the flag carried into battle by Canadian troops. Given the nature of the unit it is very likely that the Red Ensign would have been flown at this ceremony.
At the "graduation ceremony" the national flags used are the US Flag and the British Union Jack. The Canadians would have used the "Red Ensign", a field of red with a Canadian shield, and the "Union Jack" (as Canada is a member of the Commonwealth) in the left corner.
Major Crown informs Colonel Frederick that he and many of the Canadians fought at Dunkirk. In fact only one Canadian battalion of the Hastings and Prince Edward Regiment served in France (not the PPCLI as seen in the film.) It was part of the 2nd British Expeditionary Force and never reached as far east as Dunkirk but was evacuated in Operation Ariel through Brest. While it is possible Crown and a few men might have served directly with the British, the claim that many of the Canadians were at Dunkirk is improbable.
When the Canadian contingent arrives at the training centre (to use normal Canadian spelling), they are marching to bagpipes, but at far too fast a pace. Most pipe marches have a maximum pace of no more than about 90 paces per minute, but the pace in this scene appears to upwards of 140 paces or so. Also marching at that pace using the traditional British style of swinging each arm to shoulder height (which is the Canadian custom), is very difficult and awkward looking. It is highly unlikely to have been done at that speed in the Canadian Army, either then or today.
The movie's opening credits shows the copyright date to be MCMXLVIII in Roman numerals, the meaning of which is 1948. The correct copyright in Roman numerals should read MCMLXVIII, meaning the actual copyright date of 1968.
Canadians do not consider the term "Canuck" to be disparaging. If they did, there would not have been an aircraft flown by the RCAF called the CF-100 Canuck nor would there be an NHL Hockey team called the Vancouver Canucks. However, many Americans do consider Canuck to be a derogatory term, and use it as such.
The goof item below may give away important plot points.
When Major Crown approaches the group of surrendering soldiers and an officer near the end of the film, the soldiers have their hands raised high into the air, but the officer stands with his hands behind his back - with no one challenging him to raise his hands, too. This is a breach of normal procedure, and common sense, and leads to fatal results here when the officer uses a gun he had hidden behind his back.