The Devil's Brigade actually existed; its formal military designation was the First Special Service Force (FSSF), and alternatively known as the "Black Devils". It was indeed a joint American-Canadian unit, was comprised of three regiments of two battalions each, and was envisioned for difficult, cold-weather, mountain-warfare missions. The members were known as "Forcemen". Initially earmarked for Northern Europe, the FSSF was first sent to the Pacific, then to the Italian campaign, before finishing its service in southern France in 1944. During World War II, the brigade suffered casualty rates of 39%. Upon disbandment in 1944, each nations' Forcemen were incorporated into their national armies. Veterans of the Devil's Brigade have been meeting each year since 1945, in Montana, at the former training facility depicted in the movie, although in the movie, filming took place in Utah, as a stand-in for Montana.
The First Special Service Force is considered to be the predecessor to the US Army Special Forces (aka The Green Berets).
When O'Neill arrives, the regiment patch on his shoulder reads PPCLI. This stands for the Princess Patricia's Canadian Light Infantry, a real regiment, named for Princess Patricia of Connaught. It originated in Ottawa, Ontario, in August 1914, later based in the area of Edmonton, Alberta, and continues as an active unit as of 2015. The "Patricia's" celebrated their 100th anniversary in 2014.
On the 30-mile hike, Maj. Bricker (Vince Edwards) tells the US troops, "Alright now--look alive! I know this is route step, but shape up!". "Route step" is a marching maneuver where troops don't have to keep cadence (stay in step) but should keep distance, interval, and alignment. This is similar to "At ease, march" but you are allowed to talk. Route step is primarily used when marching over bridges that may or may not be safe. Marching in cadence could create sympathetic vibrations in the bridge that could cause a collapse.
Much is made of Lt. Col. Fredericks' lack of combat command experience, but the fact is that prior to the invasion of North Africa in November 1942 there were very few officers in the US Army who had been in combat. In terms of his experience, Fredericks was no different than the vast majority of battalion and regimental commanders who were given commands in 1942.