When they first arrive at The Building, they park on O'Keefe St, which is clearly a 2 lane, undivided, one way street - just as it is in reality. In the shot showing them entering the building, the street behind them is a 4 lane, divided, two way street - because the interior was filmed elsewhere.
Although the in-universe location of The Building is given as "156 Prospect", when the Tinker exits the building, the intersection shows the names of the real life cross streets: Common and O'Keefe.
When they first arrive at The Building, there is a shot looking up, followed by a shot looking down from the roof. The roof shot does not match the geography, as the building is flush with the sidewalk, and on a curved street - but the camera from the top of the building shows a straight street, and a building which is set back from the sidewalk.
When they are headed back to The Building on nuked Earth, The Building in the background is 4 floors shorter than it should be. During this same scene, the CGI ruins in background also change between shots.
When Tinker is showing the video footage of Alex coming out of The Building, the double door is missing, he is just walking away from a single window - this is because in reality there is no door on this side of the building at all, and they forgot to add the CGI door to this footage.
When the car runs out of gas, they are travelling west on S Peters St, New Orleans - away from the Market Street Power Plant, but also away the CBD. In reality, the ruined building in front of them to the right is the same ruined building shown next to The Building when they first arrived, located at 1738 S Peters St - the same graffiti and air conditioner are visible, although the CG ruined sections are different.
At the start of the film, as Ronan is at the Greyhound bus station, a building is focused in the background - this is not The Building, which is not visible from here, but is instead the Hancock Whitney Center - known as One Shell Square at the time of filming. While it looks similar, it has 51 floors, while The Building only has 31 floors.
The film is set in New Orleans, which is below sea level, and kept from flooding by a levee system which includes pump stations which constantly remove water from the city. If New Orleans was nuked, it would be under water, as it was when the pumps failed during Hurricane Katrina.