There are some rank insignia mistakes. Number One is introduced as "Lieutenant Commander Una Chin-Riley" yet she is wearing the rank insignia of a full commander: two full stripes. A Lieutenant Commander's rank insignia is a full stripe under a thin stripe (in TOS it is a full stripe and a staggered stripe). It is not uncommon for a ship's first officer to be a Lt. Commander if they have not been in the position long.
Spock at this point is a Lieutenant but he is wearing Lieutenant Commander's stripes; a Lieutenant just has one stripe. La'an is the ship's chief of security and the ship's second officer. She is also wearing Lt. Commander stripes but is addressed as a Lieutenant, but it would make more sense for her to be a Lieutenant Commander. Either way both of their rank insignia are not matching the rank they are addressed by.
Ortegas is addressed as a Lieutenant but is wearing Lieutenant Commander's strips. A Lieutenant Commander may be addressed as a Commander or Lieutenant Commander but never as just a Lieutenant, so either her rank insignia or the manner she is addressed by the rest of the crew is in error.
