(at around 49 mins) In the car chase scene, Captain America takes over the car by punching out the windshield. Yet, in every shot of the vehicle afterwards, the reflection of light can be seen on the "nonexistent" windshield.
Throughout the airport fight scene, Black Widow's shoes alternate between heeled and flat-footed.
Captain America and Bucky fly from Leipzig to Siberia, presumably in a number of hours. Meanwhile, Stark is able to fly to America, watch Rhody get an MRI, converse with Natasha at Avengers headquarters, fly to the underwater prison and meet with the captured Avengers (who are already imprisoned), and then fly to Siberia only to arrive shortly after Captain America and Bucky.
(at around 21 mins) When Secretary of State Thaddeus 'Thunderbolt' Ross is going through the various places that have been destroyed (Sokovia, Washington, etc) Tony Stark is sitting in the background. In one scene he has a wedding ring on. Said wedding ring disappears in the next shot.
(at around 51 mins) Towards the end of the foot/car/motorcycle chase in the tunnel, the SUV that Captain America drives and leaps from as it crashes starts to roll. One of the front doors is open and is almost immediately torn free as the vehicle rolls; in the next shot, a longer shot from further back, the vehicle is intact with all doors closed.
The "Sokovia Accords" are concluded in Vienna. By international diplomatic protocol, accords are named for the location where they are signed, not for what they are about.
Even though the capture of Bucky takes place in Romania, German Police special forces (GSG-9, anti-terrorism unit of the Federal Police) are the ones to make the arrest. While they do operate outside of Germany under certain circumstances, it is highly unlikely that they would do so in this case since Bucky is a US citizen. Also, Romania has its own special forces unit, the BSIJ.
At 1:10 in the HYDRA clinic the IV needles are all pointing towards the hand. If this were done for real no medication would go into a patient as it would be fighting the flow of the blood in the vein. IVs need to point towards the heart to go with the flow of the blood.
(at around 1h 8 mins) When Bucky jumps into the helicopter, he begins flying away in a matter of only a few seconds. In reality it takes a minimum of 90 seconds to two minutes to bring a turbine engine up to operating speed and temperature before take off can occur.
In the extended version of Peggy's Funeral (on Blu-ray) the procession in the church shows four men of the Household Cavalry (uniform is that of the Blues & Royals)following the casket. They are wearing helmets, with red horsehair plumes: this is contrary to British (and Commonwealth) military protocol. Head coverings are never worn inside a church; they would have been removed in the Narthex (vestibule) and left there, along with their sabres (which are not visible, but weapons are never carried inside a church, unless the soldier is on an actual protection detail).
(at around 30 secs) At the HYDRA base in 1991, the code to enter it is shown as '17826.' However, when Zemo enters the base towards the end of the film (at around 1h 50 mins), it appears as though the last 2 digits that he enters are '86.' However, it's a different door, as in 1991 it was a vault to store the red notebook, and in 2016 it was a door into the HYDRA facility.
(at around 31 mins) When Steve Rogers receives his sad news text, it originates from a London-based landline phone number and not from a mobile/cell phone. The technology to send SMS text messages from landlines has been available since at least 2013.
During the opening scene set in 1991, the computer monitors surrounding Winter Soldier do not appear to be of that year. However, previous installments have shown that secret societies such as SHIELD and HYDRA have access to technologies that the rest of the world doesn't have yet.
(at around 1h 9 mins) Even if Steve's enormous biceps are strong enough to hold back a copter, it would easily be able to take off between the time that he latched onto it and the time that he grabbed the rail. He provides no anchoring at this time, other than his body weight. That wouldn't be nearly enough to hold the helicopter down for as long as he does.
However Steve weighs about 240 pounds and when he jumps to grab the skid he is seen swinging on it violently. It appears the aircraft is a Eurocopter AS350 which is a light single-engine helicopter. Bringing a helicopter in a stable hover requires precise simultaneous control inputs. It is conceivable that when Steve was swinging his body weight on the skid that destabilized the helicopter enough and Bucky had to focus on keeping it stable rather than increasing the power for take off.
However Steve weighs about 240 pounds and when he jumps to grab the skid he is seen swinging on it violently. It appears the aircraft is a Eurocopter AS350 which is a light single-engine helicopter. Bringing a helicopter in a stable hover requires precise simultaneous control inputs. It is conceivable that when Steve was swinging his body weight on the skid that destabilized the helicopter enough and Bucky had to focus on keeping it stable rather than increasing the power for take off.
(at around 2h 5 mins) When the characters are talking outside in Siberia, no one's breath is visible.
(at around 43 mins) In a Bucharest-set scene, in the background there is a building that says FARMACIA. This is Spanish, not Romanian. The Romanian translation for pharmacy is farmacie.
(at around 19 mins) When King T'Chaka of Wakanda is speaking in the UN council, there is a clearly visible reversed word written in Arabic that means "Nations," and its letters are also not joined together, which is wrong in Arabic language.
During the face-off between Bucky, Captain America and Iron Man at the end of the film the fake snow is seen stuck to the actors after they fall down. It remains throughout the scene rather than melting as real snow would.
(at around 10 mins) During the fight, the face of Scarlett Johansson's stunt double is briefly visible.
(at around 2h 20 mins) The character of Colonel James Rhodes is credited as Lieutenant James Rhodes.
When Bucky knocks the car off the road at the beginning, he strikes the car hard enough to knock it off the road, but leaves no dents in the fender or door.
(at around 1h 29 mins) When confronting Steve Rogers at the airport, Tony Stark states that he was given orders to arrest him 24 hours prior. Therefore, in that time, Stark was able to fly to New York, recruit Peter Parker, get him a valid passport, design and create a costume for him, and return with him to Europe.
In the Bucharest market scene, Bucky is seen picking up a news paper titled "Jurnalul de Lugoj", which means "The Lugoj Journal". Lugoj is a city in western Romania, 310 miles from Bucharest, making it unlikely for a local news paper to be sold in Bucharest, especially in a small market stand.
When King T'Chaka of Wakanda is speaking in the UN council, there is a clearly visible reversed word written in Arabic that means "Nations", and its letters are also not joined together, which is wrong in Arabic language.
The sleeve patches on the Russian soldiers in the beginning showing the flag of the modern day Russian Federation. The scene took place on 16 December 1991, the USSR was still in existence (though only for another 10 days). The soldiers would have had a red hammer and sickle on their patches instead.
Although huge parts of the movie were shot on location in Berlin, there are no real existing Berlin buildings to see. The government buildings in the so called »Spreebogen« (helicopter combat scene on roof top) have a similar appearance and almost agree on the situation, but in the movie they are much higher and »darker« than in reality. However, the »Reichstag« (German Parliament) is in the wrong place in the movie and also carries an architecturally completely different historical dome and not the real existing modern one designed by Sir Norman Foster. The only building that exists in the film as in reality, is the ICC (International Congress Center), which was moved to Romania in the film and serves as the backdrop for the car chase with the German police / GSG-9 unit. As noted by others here, it is very unrealistic that the German Special Forces Unit GSG-9 is deployed in Romania. Also, the number plates attached to the German vehicles do not correspond to reality.
Tony's parents go away for Christmas and tell him they'll be back "Monday." They were killed on December 16th, which is 9 days before Christmas. There is no way they could be gone for longer than a week and still be back "Monday."
(at around 6 mins) During the opening battle against Crossbone's men, Rogers identifies several operatives as carrying "AR-15s." The AR-15 is the generic designation for the semi-automatic version of the M-16 and is produced by several companies worldwide. Crossbone's mercenaries are seen carrying Galil MARs, SIG 550s, DSA SA58 OSWs and M4 carbines, everything but AR-15s.
When T'Challa is checking to see if his father is alive, he feels for a pulse with his thumb. Vital signs cannot be checked the way because the thumb has its own pulse.
News reports refer to Bucky as the Winter Soldier. In the previous film, this was a nickname for him, known only to the intelligence community, in which his existence was only a rumor. This epithet would be unknown and have no meaning to the general public.
The pieces on the chess board in the Avengers' compound are positioned on the wrong sides of the board. The left corner field (A1, H8) of the chess board has to be black (not white), therefore the board has to be turned 90 degrees to be correct.
When Vision is cooking paprikash for Wanda he is reading from a recipe on paper. Since Vision is an android he has a computer for a brain. Once he found a recipe he should have it stored in his memory and therefore not need to refer back to a hard copy.