The sign on the door behind Raj lists Ann Shea's name. Ann Shea is the set decorator for the show.

Leonard: So, when Howard said the FBI would be contacting me, I was expecting Mulder. Glad to see I got Scully.
Angela: Who?

Leonard: I'm going to pick you up at 8:00, show you a night you will never forget.
Angela: Sounds great.
Leonard: Really?
Angela: Yeah. Can my six-foot-two Navy SEAL husband come with us?

Sheldon: 18 years ago, I sent the FBI Crime Lab samples from a bag of excrement that had been lit on fire on my front porch for fingerprinting and DNA analysis. Why haven't I heard back yet?
Angela: Well, the FBI Crime Lab does have a lot on its plate.
Sheldon: That's of little comfort to a nation attempting to scrape burning feces off its shoes.

Penny: For example, Lisa Peterson hasn't talked to me since the 11th grade, because no matter how much you apologize, you can't go back and un-dry-hump someone's boyfriend.
Sheldon: You're saying I'm facing Starfleet Academy's unwinnable command scenario: the Kobayashi Maru.
Penny: Exactly. Sometimes you can't win.
Sheldon: Captain Kirk won.
Penny: Kirk cheated.
Sheldon: Impressive that you know that. It's hard to believe I'm actually having this conversation with you.
Penny: Right there with you.

FBI agents don't do background checks, that is handled by the Office of Personnel Management (OPM).

Sheldon: (Speaking about Howard to the FBI agent) He crashed the Mars rover while attempting to impress a woman...

In episode 2x08 The Lizard-Spock Expansion, Howard took a date to the Mars rover control room hoping to impress her.