Factual error: Wanda's father opens his briefcase of DVDs and one of them is Malcolm in the Middle. But the bomb that killed him fell in 1999, and Malcolm in the Middle didn't start airing until 2000.
Plot hole: The protagonist gets in the exclusive, multi-millionaire, invites-only auction because the invitation is on a printed letter that he faked. This means that the guards at the entrance don't have a guest list to check, and since nobody knows who this person is, the staff does run a background check on his identity when he makes the first outrageous bid...by looking his name up on Wikipedia. That's mighty low standards of security, especially for an auction that was supposed to be for a selected audience and the most important in France.
The Man with the Umbrella - S1-E3
Plot hole: With all the cameras and guards watching, there's no way anyone would be able to use a cigarette lighter to help them pass the game.
Power Broker - S1-E3
Factual error: Every guard in the prison has the emblems of Hamburg on his/her shoulders of the uniforms. Zemo is said to be imprisoned in Berlin, so they are wearing the wrong emblems.
What If... Captain Carter Were the First Avenger? - S1-E1
Deliberate mistake: When Peggy and Steve are studying the map where the 107th Army division is held captive, the names on the map are nonsensical names that do not even follow German spelling or standards for place names ("Farfignugen," "Dädtenorth," and "Rosskjhberg," for instance). Most of them are also reused, appearing several times on the same map. This is most likely done deliberately so as to avoid any resemblance to real places, but still looks out of place and illogical. (00:11:27)
Battle Scars - S1-E7
Continuity mistake: When Echo prepares to calibrate the surgical pod, he has a bandage on his head, even though the members of the Bad Batch don't get their control chips removed until near the end of the episode. (00:14:11)
The M.O.D.O.K. That Time Forgot! - S1-E2
Character mistake: M.O.D.O.K. refers to Hoobastank as "the Beatles of the late 90's." Hoobastank only released one album in the 90's, and they didn't become popular until after they released their second album in 2001.
Visible crew/equipment: At the end, when Aunt Vi and Delilah return home, just as Miles walks into the house, the green T-mark is visible on the floor.
Plot hole: Loki states while on trial that The Avengers should be on trial for traveling through time to change the timeline. How did he know they came back through time?
Suggested correction: He recognized that there were two Tony Starks in the lobby by the smell of their colognes, and combined with all the other unusual shenanigans going on, he correctly deduced the Avengers travelled through time, though he incorrectly thought it was to prevent his ascendancy.
How exactly do you distinguish the smell of cologne as belonging to two separate people? But besides that, it's pretty wild to jump to a conclusion about time travel when it could be that someone else happens to be wearing Axe.
I'm sure he simply recognized his voice.
Stego Search - S1-E7
Continuity mistake: Four people (a guy in a pink shirt, a girl in an orange dress, a guy in a blue shirt, and a girl in a denim skirt) stand up from a picnic blanket to go listen to a guitar player. However, in the next shot, the girl in the denim skirt and the guy in the blue shirt are replaced by a girl in a black dress and a guy in a green shirt, and they are never seen again.
Factual error: A passerby tells Sheldon Sampson that the stock market has just gone "tits up." This is a British expression that you would likely not hear in the United States, and you certainly wouldn't hear it in the 1920's.
Continuity mistake: When Chrissy and Lois are in the car before going into the meeting, the passenger side window is down, but not all the way. But in the next shot when Chrissy steps out, it's all the way down.
Audio problem: After Kate shoots an arrow at the mafia guys, she says "told ya." Then we hear Clint/Hawkeye say "yeah", except he's on camera and his mouth doesn't move, he doesn't even change his facial expression.
Chapter 7: In the Name of Honor - S1-E7
Revealing mistake: When the big battle starts, Boba and Mando appear using their jet packs. As Boba lands with one foot forwards, sand is thrown up into the air, but the sand is a special effect coming from about a metre in front of Boba, not from the foot itself. The result is very unconvincing.
Visible crew/equipment: After Raines shares details with Kellett about Semien's crew, when it cuts to Semien waking everyone up, just as he announces his contact with Belgian Federal Police, there's a visible T-mark taped to the floor behind Andre's cot. (00:24:25)
Factual error: When Alina stands outside of the door to the banquet hall, waiting to demonstrate her power to the king and queen, there is a modern electronic occupancy sensor on the wall behind her.
Revealing mistake: Whenever the newspaper Josh is shown at the beginning appears, the news story consists of a paragraph that repeats itself.