Factual error: Major Markham is consistently referred to as the CO (Commanding Officer). As a company commander, he is actually the OC (Officer Commanding). In the British Army, CO is a title reserved for the commanders of battalion-sized units.
Factual error: Sergeant Baxter seems to be the senior NCO of the company. There appear to be no company sergeant major or staff sergeants. This is very odd, but particularly odd in the Royal Military Police, which is very NCO-heavy.
Factual error: The Royal Military Police's main job is to police the army. The show depicts them as a general security unit. Weirdly, when soldiers are shown guarding the prison and the courthouse, which would be an RMP job, they are not RMP.
The catalogue of errors made by the SAS team (e.g. being caught out in the open, not posting a watch, not using cover) would be unlikely to be made by an ordinary trained infantryman, let alone an elite special forces unit.