Purbright is listed as a full colonel and referred to as Brett's senior officer, yet they both wear the rank of a lieutenant (half) colonel.
Reggie Soper is addressed as 'sergeant' throughout the series, but wears the rank of a staff sergeant (three stripes and a crown, as opposed to the three stripes only of a sergeant) and should therefore be addressed (given that he is is the Royal Army Medical Corps) as 'staff'. Though, as he is in charge of the quartermaster stores, he would usually be addressed as 'Q'.