When Ryan holds his gun to Cooper's head during the 'special forces selection' scene at the beginning of the film, the magazine is clearly not inserted. Ryan goes on to shoot a dog with this same weapon seconds later.
When Ryan is thrown across the table, the sword is shown being knocked to the floor. But when Ryan gets up and puts his arms on the table, the sword is back on the table. Then the next shot, the sword is on the ground again and Cooper is reaching for it.
After Spoon has reported the status on their ammunition, Cooper places his gun on the table. In the next shot, two bandages suddenly appear beside its hammer. This is true in wide screen tv as in full screen, the hammer is cut off before it cuts to the shot with bandages.
Throughout the first half of the film, when the squad is armed with the standard British rifle, the SA80, Cooper holds the weapon in his left shoulder. The SA80 is always held in the right shoulder, even if the user is left handed.
The group of soldiers are referred to a 'squad'. 'Squad' is not the name given to a small infantry unit in the British Army, it is called a section. Also sections have 8 men minimum, not 6, and generally are commanded by a corporal.
When Megan rescues the soldiers in her truck, you can see stationary scenery such as trees through the passenger windows visible in the background of the closeups of her and Pvt. Cooper, despite the actors all bumping and swaying to suggest being in a moving vehicle.
In the farmhouse, when Cooper is reloading the MP5 magazines with new bullets, at the kitchen table, the ignition caps already have firing pin impressions on them, showing them to have already been fired.
When the team reaches the destroyed special forces position there are 105mm charges and ammunition amongst the equipment present. The 105mm is an artillery piece unlikely to be used in a wood, and definitely not by special forces.