The men suffered heatstroke following a 16-mile (26km) exercise in the Brecon Beacons in July 2013 and failings on the expedition were described as “some of the most significant”, a health and safety inspector had seen.
Two of those in charge of the march, who can only be identified as 1A and 1B, deny negligence and are appearing before a court martial in Bulford, Wiltshire.
1A was the training officer in charge of the march, and 1B, a former warrant officer, was the chief instructor on the exercise.
Lance Corporal Edward Maher, 31, Lance Corporal Craig Roberts, 24, and Corporal James Dunsby, 31, died after an exercise lasting eight hours and 45 minutes when they carried up to 27kg (4st) on their backs on one of the hottest days of 2013.
The Court Martial Centre has been told that inquiries since the three deaths have identified systemic failings.
Health and safety inspector Sarah Baldwin Jones told the court: “There were very serious failings, they were widespread failings.
“Probably some of the most significant failures I’ve come across in many years in dealing with the Ministry of Defence.”
She said there had since been a “complete and utter lack of training” on the Ministry of Defence’s guidance – known as JSP 539 – on heat illness.
The inspector said: “From my investigation and subsequent investigations I don’t think there was any training provided on JSP 539 to anybody in the Army or anybody in the JSP units.”
Ms Baldwin Jones said there was not enough awareness of JSP 539 and exercises in heat was “not currently able to be defined”.
She said if there is only one casualty suspected of suffering heat illness, the document states that stopping the exercise must be considered if the operational environment allows but often this was not possible.
Ms Baldwin-Jones said her report identified multiple failings that could not be attributed to one individual.
The trial is expected to last three weeks and will be adjudicated over by a panel of military personnel.