In the very first scene, the song "If You Leave Me Now" is playing in the background when Barry is at the coffee store in Central City. Then he goes to Gotham City, where he stays at least six minutes (as shown on Barry's wristwatch). When he leaves Gotham and runs back to the coffee shop at Central City, the same song is still playing in the background. The song's length is less than 4 minutes.
The first time young Barry runs at full speed, his clothes burn off. Each additional time he runs at full speed without the Flash suit, his regular clothes are fine.
When the Flash is saving the babies, he takes a bite out of a burrito before using it to deflect some knives. When the burrito hits the knives in a later scene, it appears to be fully intact.
During Batman's fight scene in the Soviet bunker, he uses his grappling hook to pull a soldier hiding behind a pillar. Despite being distant from the soldier, the next cut shows him oddly teleporting closer so he can kick him.
When flash glues back his tooth it's the left one. When it falls out at the end of the movie it's the right tooth.
When the projectiles from the AK-74s are seen by Barry they lack any rifling marks. Rifling is required to stabilize a bullet in flight.
Bruce Wayne is playing Chicago's "25 or 6 to 4" when the two Barrys arrive in his manor. The record player shows the needle near the end of the album side. In fact, "25 or 6 to 4" is the second song on side 3 of the two-disk album CHICAGO (1969) and the needle would have been closer to the beginning of the side. However, he is in another reality, where the album order could be different.
Near the end after the court scene, a pan around the street shows two different pizza shops. One says "Gotham Pizza", but the court would be in Central City, Barry Allen's home city. However, just because it is named "Gotham Pizza", doesn't mean that it has to be located in Gotham City. "New York Pizza" is popular all over North America, and Gotham is broadly based on New York.
On young Barry's computer in the new timeline is a Looney Tunes screen saver, featuring Bugs Bunny and the gang. The title is misspelled as "Looney Toons." This spelling could be an intentional sign that things are slightly different in this new universe, even though it's not pointed out.
It is not possible to suture a wound on one's own arm with one available hand only as it requires making stitches which involve at least one knot... and therefore two hands. How do amputees tie their own shoes? You create a loop and pass the end through the loop. Easy peasy.
The front part of the hospital building drops relatively vertically and yet the nurse and the babies' cots are seen sliding down and rolling down at a steep angle.
When stitching his own arm, Batman uses the wrong instrument: it is not precise enough to properly hold the needle and keep it firmly in place when going through the skin.
Very poorly animated CGI stand-in for the babies falling from the hospital.
When the Flash takes a baby out of a microwave that he had previously put inside to protect it, the baby is a poorly animated CGI stand-in.
The way Barry's feet slide on the road while running at high speed show poorly animated green screen technique.
When both Allens are searching through the dilapidated Wayne mansion, the Chicago song, "25 or 6 to 4" is heard playing, which is the second track on the third side of the album "Chicago," but the needle on the vinyl disc is shown playing at the end, at the point of the inner groove, which normally has no music.
It is heavily implied that Barry needs to eat a massive amount of calories to retain his super speed at the beginning of the movie. However, this requirement is dropped for the end fight scene, in which the paradoxical Barry attempts to win the fight in an endless loop.
There wouldn't be a package labeled "Confidential Exhibit" left on the floor outside of Allen's apartment.
Even though Kara Zor-El has been a prisoner of the Soviets since she arrived on Earth, she loses her Russian accent after her first few lines of dialogue.
Technically, Terraforming means shaping a planet like the Earth to make it habitable by humans. So Zod is not trying to Terraform Earth but to Kryptoform it.
Barry Prime, in an effort to find help fighting Zod, tries to look up Cyborg, Aquaman, and Wonder Woman to no avail. They weren't really known to the world during the events from Man of Steel (2013), so even if they were in the new reality, he still wouldn't have been able to find them. They were all introduced (including Barry) in Batman v Superman: Dawn of Justice (2016), and even then didn't really become known until the events of Justice League (2017).