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.
During the crane scene at the start, there is a difference between what the camera shows when the notes are being wrote down and what is shown when the waitress asks the Observer if the language he is writing in is Korean.
During the initial crane collapse, and only visible for about a second, the sign on the crane's crossbeam indicates that it is the property of the series' fictional corporation "Massive Dynamics Corporation". That connection is never mentioned in the episode. Furthermore, it relates to another series trivia item, in that the pluralized version of "Dynamics" only existed in an earlier series pilot script, and the "s" was dropped for all actual series references. Also, the series never depicts the name with the "Corporation" suffixing, thus, making the crane's signage doubly incorrect.
When the Observer is using his binoculars during the crane scene the text that pops up on the write of the heads up display is part of the code of a shell script that traverses directories in a Unix-like operating system and has no relevance to the actual scene and would be pointless in any type of heads up display.
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.
At the diner, the Observer orders 11 jalapeños. The server brings him 11 slices not whole ones.