Corrected entry: Judging by Wonder Woman's powers and abilities shown at the end she could've taken the photo that she wanted from Lex Luther any time she wanted without sneaking about.
Correction: Diana had no idea where the physical photo itself is. Taking into account the year the photo was taken, and confirmed by it's reveal in Wonder Woman, the images on on a glass plate. Those cannot be duplicated, at least not easily, and the photo itself would have been one of a kind. She didn't just want a digital copy of the image; she wanted the original glass plate - which she had no idea as to the location of. What she wanted was to find the information on where it was being kept so she could go retrieve it.
Corrected entry: This is supposed to take place 18 months after the fight between General Zod and Superman where much of Metropolis was destroyed and leveled, especially where the remains of the World Engine lie, but the city looks completely untouched by these events.
Correction: The statement, "a good portion" of Metropolis has been destroyed, or its permutations, is a fallacy that people continue to promulgate. Observation of key images in Man of Steel, most prominently the point of view shots of the approaching military planes or the images of the city from Zod's ship, wil show that a very small percentage of the city was actually affected - no more than a few square blocks. This fallacy supports a common narrative but it does not meet with observable evidence.
Corrected entry: Lex Luthor was thrown into Belle Reve prison at the end of the movie, the very same prison that the Suicide Squad are recruited from in the upcoming movie.
Correction: In the extended cut, Batman tells he's sending him to Arkham Asylum, not Belle Reve.
Correction: There is no statement or evidence of any kind to support the idea that Luthor is in Belle Reve.
Corrected entry: Batman has 3 minutes to change out of his armour, get in the Batwing, find out where Martha is being held, fly there, beat up all the bad guys guarding her, and then save her - no chance.
Correction: He seems to get out of his armour and into the Batwing quickly, but we just don't see him making the change. We see the timer at 10 minutes when he's already in flight - given he just has to fly across the harbour, and clears out the bad guys fairly swiftly and in mostly real time, he's got enough time to do it.
Correction: We only know two pieces of time data: Luthor tells Clark he has, "less" than an hour when he leaves him on the Helipad. At one point before the fight starts we see the clock has about 30 minutes on it. And when Batman arrives he has 10 minutes left. The complete passage of time is not charted but we are shown how much time is left at various points.
Correction: There are no powers that indicate she could have gotten the photo any other way. She has great strength, a sword, shield & her lasso, but they don't show any magical powers that would have allowed her to just get the photo, and storming the place and destroying/stealing the photo would have run the risk of exposing herself even more than a single photo might.