In several photos depicting events that supposedly occurred in 1987, A US Marine is shown wearing the US Army's Army Combat Uniform (ACU), which was not fielded until 2005, and the Advanced Combat Helmet (ACH) which was not fielded until 2002.
Agent Dunham asks Col. Jacobsen about 1987 at Quantico. When Jacobsen shows her a picture of Master Sgt. Stewart Malik, he is obviously wearing digital camouflage utilities which were not adopted by the Marine Corps until 2003.
At one point we are told a story of a Marine at Quantico in 1987. When we see him pictured, his equipment is modern and his uniform / camouflage is recognizable as the ACU. This uniform is used by the Army, not the Marines, and was issued in 2005.
When Peter is taken to the graveyard to dig up the cylinder, we are to assume it is his grandfather's grave. However, the date of death is listed as 1944, while Walter's DOB is given as 1946 in the pilot.
When Olivia shows the picture of the Observer in the hospital, his positioning is different when she shows it to Peter from when she shows it to Broyles. When Olivia shows Peter the picture, the Observer is seen from the front, and when she shows it to Broyles the Observer is seen from the side, standing around the corner from where he stood when Olivia showed Peter the picture.