When Bucky catches Sam's nephews playing with Captain America's shield, the children hurriedly put the shield back in the bag without closing it, and when they set it down, its front side is facing down while still being in the bag. Moments later, the shield now sticking partly out of the bag and the front is facing up.
In the first scene, when Bucky and Sam are confronting John Walker, Walker says, "You don't want to do this." To which Bucky replies, "Yeah, we do." and immediately advances toward Walker. The following shot is a wide angle from above showing all three but Bucky is standing still and doesn't advance until after Sam does.
At 38'00 the shield slides down the wall onto the floor "facing" down but at 38'10, it is now "looking" up.
When Bucky, Falcon, and John Walker are fighting, the shield is knocked away from Walker and lands slightly propped up off the ground (by the volume of the leather straps on the back side). In the next shot it is laying completely flat.
Captain John Walker is given an Other Than Honorable Discharge from the Army. Enlisted soldiers are given discharges. Commissioned officers expelled from the military are "Dismissed."
When Captain John Walker is being reprimanded by the council, he is wearing a Combat Infantryman Badge (CIB) with a star, signifying 2 awards. Given the time period and his age/rank, he should instead wearing a badge without the star. He would have to have been in the military since at least 1994 and have served overseas in both Somalia and the War on Terror to qualify for two CIBs.
On the boat, when they are showing the family photos taped to a bulkhead, there is a plaque with emergency information, and the boat's name, while only partially visible, is wrong.
When Sam and Bucky are walking and talking after the shield training, Sam carries the shield on his left arm. The shield does not cast a shadow on his body, as it was a CG effect added to the shot.
During the fight between John Walker, Falcon, and Bucky, the Captain America shield can be seen flexing at several points, revealing it to be a prop made of soft safety material. A corrected version of the episode was later uploaded that used CGI to fix most of these occurrences.
When Torres calls Sam while Sam is watching the news, the audio from the TV cuts off before Sam grabs the remote to mute it.
When John Walker is assembling his homemade shield, the center part (blue circle with a silver star) is seen surrounded by a white circle, while he has spray-painted two larger circular pieces (which have yet to be welded together) red. The Captain America shield features a blue center surrounded by a red circle, then white/silver, then another red circle for the outer edge. When this shield appears fully assembled in the next episode, the color pattern has been corrected.
During the training montage Sam is shown repeatedly struggling to control Cap's shield yet earlier both he and Bucky were playing with it together without any such difficulty.