In the first season Lydecker and the others from Manticore after Max don't know what she looks like and it's a big deal when there's finally the reveal and they can make a drawing to send to Seattle Police to catch her. However, in season 2 they introduce that there are multiple clones of her, one full grown, so they should have known exactly what she looks like.
You can often see the wires when characters are running up the walls or flying around the room.
When Logan calls Alec's phone in "Borrowed Time" you can still hear the phone ringing after Alec's voicemail answers the line.
The true Gillette, Wyoming is in a sage brush desert - nothing like the forested mountains of Vancouver.
Max' surname Guevara is pronounced Guevera every time it is spoken.