Olivia states that she's been a cop for 20 years while on the stand. She's actually been a detective for 20 years. She was a cop before she joined the SVU team as a detective. Not necessarily a mistake, but something worth noting.
In the opening scene when discussing the 5-year old boy stabbed, the uniformed officer tells Olivia and Fin that the "boy was taken to St. Vincent's". St. Vincent's Hospital on 7th Avenue in Manhattan closed in 2010. The facility has since reopened as a satellite of Lennox Hill Hospital, part of Northwell Health System -- but no actual hospital is named St. Vincent's in Manhattan or Westchester County since the 2010 closures.