The series ends as it started, with Lt. Provenza heading the major crimes division.
Final show of the series.
Sanchez was in fact a Detective Sergeant. He was just always referred to as Detective. In The Closer episode 7.2 (Repeat Offender) after the funeral you can see the Sergeant bars on Sanchez's uniform. This makes his promotion to Lieutenant correct. As for Buzz, he had been a reserve officer, and was to go through the academy. After the academy he was going to be a Probationary Detective. This may or may not be something "allowable", but considering his time in Major Crimes, it may also be something the Chief of Police and the Mayor could authorize. That's just a thought on Buzz, but accurate on Sanchez.
With the exception of Mary McDonnell, every member of the main cast that appeared in the pilot also appeared here. In addition, secondary characters Fritz and Dr. Morales also appeared in both. All of the characters remained the same rank, except Fritz had gone from being an FBI Agent to a deputy chief. In the finale, Sanchez is promoted to lieutenant and Buzz is made a detective.