(at around 40 mins) During the chase scene in Budapest, when Natasha is attempting to steal the minivan, an enemy Widow shoots out the front windshield. A few shots later, the windshield is perfectly intact.
(at around 40 mins) The blue BMW get entirely scraped and dented on left side when escaping the gunfight. Few seconds later, as the car is driving by, the left side of the car is shown in perfect condition.
(at around 44 mins) During the flashback scene in Budapest, which takes place before The Avengers (2012), Natasha seems to be wearing the exact same arrangement of earrings that she wears throughout the rest of this movie, revealing that the crew may have forgotten about changing them out for the flashback scene, and possibly without thought to her earring arrangements in previous films.
(at around 59 mins) During the helicopter escape of Alexei, a machine gun in a tower shoots through all of the side windows in the helicopter, both sides. But in following shots of the helicopter in air and on the ground, they are all intact.
(at around 25 mins) When Natasha is loading up her vehicle and puts the yellow fuel can in it, she is clearly wearing white pants. She drives in her car until the scene on the bridge with Taskmaster. When she gets out of her vehicle, she is then wearing dark pants.
(at around 1h 50 mins) A human body in free-fall is not enough mass or impact to knock the tail off a supersonic aircraft of that size.
(at around 1h 40 mins) Smashing your nose doesn't sever your olfactory nerves or impair your sense of smell in any way. Nostrils full of blood aren't that much of a deterrent.
(at around 1h 5 mins) A helicopter that runs out of fuel would have to auto-rotate to make any survivable landing, which includes moving forward and gaining speed in the rotor disk. But the one shown drops straight down with almost no rotor speed. It would have been obliterated on impact, and only Red Guardian might have survived.
(at around 59 mins) In the helicopter scene, Yelena uses an XM-25 grenade launcher to take out one of the prison's guard towers. The launcher's projectile is portrayed as rocket rather than the actual weapon's non-propelled 25mm grenades.
(at around 1h 2 mins) Yelena and Natasha casually mention to Alexei that their entire reproductive systems right down to the ovaries were removed as part of becoming Black Widows. Surgically removing ovaries causes premature menopause due to lack of estrogen, which has several negative health effects including reduced bone density and mood swings.
(at around 1h 35 mins) During Nat's confrontation with Dreykov in his office, when she can't shoot him, he asks if the safety is on. Glock pistols don't have external safeties. However, Dreykov is mocking Nat for her inability to shoot him, rather than suggesting a valid reason for her being unable to do so.
(at around 7 mins) The S.H.I.E.L.D. vehicles involved in the Ohio chase, set in 1995, are equipped with LED emergency lighting, which was not known to exist at that time. However, S.H.I.E.L.D. has long had an extended variety of technology in its possession decades before the general public knew about it - up to and including the ability to shrink to the size of atoms and travel backwards in time - and LED lights at least existed in 1995, even if they weren't yet sold commercially.
Typically, recurve bows are made for a left- or right-handed archer. Taskmaster's bow appears to be ambidextrous/neutral, similar to a longbow, without an obvious arrow rest to place and tune the arrow in flight. That said, since the bow is held in the left hand the arrow should be shot from the left side of the bow. Taskmaster incorrectly uses the right side of the bow. However, the limbs of the bow somehow telescope into place, so the normal rules of usage clearly don't apply to it.
(at around 52 mins) Natasha and Yelena criticize Mason for getting them a helicopter instead of a jet. But their plan to break Alexei out of prison required a helicopter. Presumably, their original plan to use a jet was modified once they learned what they actually had to work with.
(at around 1h 45 mins) Natasha's stunt double is visible while turning her face towards the camera during her fight with the Widows.
(at around 22 mins) When Natasha is driving in Norway, you can hear a man on the radio talking in Norwegian. In fact he's talking in Swedish and not in Norwegian.
(at around 2h) When the QuinJet takes off, the camera moves to the opposite side of a tree branch as the jet's lift engines rotate and push it directly away from the camera. So the blast of the engines should blow through the tree, but the lightning bugs and leaves are undisturbed.
(at around 1h 11 mins) When Alexei is shown getting dressed, he pulls the top part of his clothing down as a unit, with all its apparent belts, clasps, & components pre-attached, revealing it to be a wardrobe prop instead of a functional superhero outfit.
(at around 1h 7 mins) Alexei tells Natasha and Yelena: "Your ledgers must be dripping, just gushing red." Loki tells Natasha in The Avengers (2012): "Your ledger is dripping, it's gushing red". It's highly unlikely that two different characters from two different time periods (and in two different films) would say the same thing to the same character. Obvious oversight on the part of the filmmakers.
(at around 11 mins) On the Cuban airfield in 1995 the soldier treating the wounded Melina has a backpack with on the outside a MOLLE system. MOLLE was introduced in 1997 and was not commonly used before 9/11 and the start of the war on terror which saw a need for more professional equipment.
(at around 6 mins) When Alexei, Melina, Natasha, and Yelena are fleeing from S.H.I.E.L.D., they drive past a high school football game. The officials in that game are wearing black officiating pants. Officials would not start wearing black pants for another 15 years. Because this scene is set in 1995, the officials should be wearing white trousers.
(at around 7 mins) 6 year old Yelena carries 2 small plush toys, they are Twilight Sparkle and Pinkie Pie from My Little Pony: Friendship Is Magic (2010), which premiered in 2010, 15 years after this scene.
(at around 1h 26 mins) The bulk of the movie takes place immediately after Captain America: Civil War (2016), which takes place after Avengers: Age of Ultron (2015). Tony Stark, who is established to be incredibly paranoid about alien invasion, has satellites in space, and invents futuristic technology, doesn't detect the Red Room, a flying base the size of several skyscrapers taped together. Neither does S.H.I.E.L.D., or any government that regularly looks for alien or even terrestrial unknown craft in the sky.
It it unexplained why young Yelena speaks perfect English with an American accent, but adult Yelena has a Russian accent. Similarly, young Natasha also speaks with an American accent, but has reverted to a Russian accent during the flashback to her defection to SHIELD.
Natasha Romanoff's proper name would be "Romanova." This error has been present throughout the character's entire history since 1964, but is especially glaring in this movie, where it's committed by fellow Russians.
(at around 22 mins) When in Norway, the car Natasha drives has a license plate that is in the wrong format. In Norway, the license plate has the format AA 12345. Her car's has the format AA 123A4.