When Mrs. Steinmetz is first discovered, she is on the floor, and later Lowenthal says she fell out of bed. But when Logan and Briscoe arrive, she is on the bed. Unless the police moved the body, which would be against all key principles of crime scene investigation, this is a major continuity error.
Police responding to any call would never allow an unrelated party to enter the subject premises, for both security and privacy reasons. The upstairs neighbor just wanders right in with the two officers.