The rank structure on that ship is pretty flat overall, and Pike himself wears the very same braid. Nothing really wrong with it: the ship has mere 200 people aboard, and the audiences of the time would certainly expect even a humble tin can to embark more. Despite the touch of silver in his hair, Pike could really be a super-junior commander of a very humble Starfleet asset, only bound for greatness over the course of his would-be televised adventures.
As is that other female character sitting on the bridge, of course...
Really, Pike is only agonizing over losing his personal yeoman, who was a lad. Plus he's extra scared of ladies to begin with, so he trips over his words all the time, which in turn only goes to prove that #1 isn't really all that different.
Except, by sheer chance, they aren't effed up at all - the character called Lieutenant wears Lieutenant braid all right! It's just that the skipper, too, is a Lieutenant, senior within rank no doubt, but not with senior rank. And nothing wrong with a Lieutenant commanding a ship, if you want to do nautical adventures in Hornblower style...
Timo Saloniemi