In the abandoned trench, the Sergeant berates his men by saying, "...this isn't a holiday camp." Although the notion of a "holiday camp" existed in Britain as early as 1897, it was not until the opening of the first Butlins at Skegness in 1937 that the term entered general usage.
The pistol used by several of the men in the movie is in fact a Webley Mk.IV, not a Webley Mk.V or Mk.VI, which would have been correct. The Mk.IV (.38 calibre version) was not designed until the 1920s.
Near the beginning of the film, the company are moving through what they believe to be a gas cloud. They are wearing the "phenate helmet" type of respirator, which was rushed into service in 1915 and was used for only a few months. By 1917 the British Army was equipped with the classic Small Box type respirator, and in fact several of the characters can be seen wearing the canvas satchel in which Small Box respirators were carried. Also, by 1917, Mustard gas was in extensive use by both sides, and in the event of a gas attack troops would have donned rubberised Gas Capes as protection from blistering agents.
Near the end of the movie, the German prisoner is pointing what appears to be a Yugoslavian Model 24/47 rifle at Private Shakespeare. However, that model did not enter production until well after World War I. The proper weapon for this scene would be the longer Mauser Model 1898 Gewehr, the standard rifle of the German army in WWI.
In his final confrontation at the body pile in the middle of the trench system, Charlie Shakespeare is armed with a German K98k carbine. But the K98k did not enter production until 1935, eighteen years after the events depicted in the film.
The gun Shakespeare uses to shoot Quinn in the end is a Bergmann MP18, a gun which was not introduced until the beginning of 1918 in time for the great Spring Offensive of the Germans. It was the first of its type to appear, so not only would Shakespeare not have found one, he would probably also have been rather surprised by it.
In one scene it shows one of the soldiers finding and later talking on a radio. This could not be possible since radios for military field use that you could talk on did not exist until WW2. The primary mode of radio communication would be by CW (Morris Code) using a telegraph type key and not by picking up a handheld microphone. In 1917 radio transmitters were large and cumbersome to operate under field conditions especially in a trench where antennas were also needed to transmit and receive radio signals.
They referred to 'The Lambeth Walk' when saying to the stretcher case - "We'll soon have you doing 'The Lambeth Walk'". This song was not written until about 1937 for the show "Me and My Gal". It was sung, and danced in World War II.