When you first recruit Molerat, you'll get the 'Happy Camper' perk, which means he will set up camp for you any time between 8PM-2AM in game as well as cook for you at any time.

Additionally, at the end of his quest (which happens after you've dealt with Benny and heard the last part of his story), he will gain 1 of 4 possible upgrades depending on how you answered his questions.

Info on Molerat's 4 special perks and how to get them (contains spoilers):

1. He Who Fights Monsters
Molerat will do more damage against ghouls, super mutants and other abominations.
How to get it - Choose 'Big Iron' as your superhero name.

2. Partner In Crime
Molerat will do more damage against all opponents, but only while you have Evil karma.
How to get it - Choose 'Deadhand' as your superhero name.

3. Bully Hunter
Molerat will do more damage against raiders, as well as anyone wearing the faction armor of the Powder Gangers or Great Khans.
How to get it - Choose 'Lone Star' as your superhero name, then tell Molerat you remember your adventures together when he asks you.

4. Billy the Kid
Molerat will do more damage against anyone wearing the faction armor of the NCR, Legion or Brotherhood of Steel. Note that this does not apply to mod-added armors.
How to get it - Choose 'Lone Star' as your superhero name, then tell Molerat that there's a lot you can't recall when he asks about your memory.