Ambulances from "Bexar County EMS" are seen, however no such agency exists. Ambulances in San Antonio are provided by the San Antonio Fire Department, with the suburbs provided by private agencies such as Acadian or AMR.
A recurring plot point is the tension between hospital administrator Ragosa and doctor TC. In fact, no hospital administrator would work from 7 PM to 7 AM as shown. Administrators interface between the medical staff and the hospital board, and a board also does not work overnight. A similar error takes place with a psychiatrist that works the same hours. A position of that nature would be on-call in the event they were needed. This was proved true when beginning in Season 2 neither position was shown as working the night shift.
Throughout the series, people keep mentioning the Texas state police. There is no such agency: Texas has a Department of Public Safety, and their uniform division is the Texas Highway Patrol.