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.
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.
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)
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)
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)
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.
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.
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.