There's an establishing shot of Manhattan (after Jessica walks away from her neighbor watching the ambulance) that shows the MetLife Building prominently in the skyline. Since this series takes place in the Marvel Cinematic Universe the Stark/Avengers Tower should be located where the MetLife Building is.
During the bar fight scene, when Luke pins Andre on the counter, Andre is holding a broken beer bottle. When the scene changes for a wider angle, Andre isn't holding the beer bottle, but then when it zoomed in again, he is holding the bottle again.
The crime occurred in a hotel. Police can't designate a witness's apartment/office as a crime scene and conduct warrantless searches even if they suspect the witness is involved.
When Jessica Jones arrives at the hospital, she tries to get past a door that's seemingly of unauthorized access. However, the glass of the doors show the 'Authorized Personnel Only' sign on the internal side so the viewers can read it instead of her.
The Shlottmans were shot at least a day before Jessica is shown riding in the elevator, but the blood on the ceiling still looks fresh.