An arrested guy that Briscoe is bringing to a Police Car in handcuffs asks Briscoe what he is being charged with and Briscoe pats him on the back and replies
"Oh Don't Worry, This One's On Us"
.

On arresting a florist's helper, to the florist:
"We'll water him once a day."

While arresting a protesting insurance company executive in the executive's office:
"On your feet pal; your plan doesn't call for a second opinion."

When he and Curtis first meet a woman just leaped to her death off an overpass.
Curtis: Pretty girl.
Briscoe: Not any more.
Later in the same episode Van Buren tells Briscoe and Curtis that the ME's tox report found only Midol in the victim's system.
Briscoe: That explains it.

One that was all in the delivery minor, but makes me crack up every time
He and Green (I think?) are interviewing someone who knew the victim in the someone's office. He's just finishing lunch and eating some super-duper chocolate cake, maybe Death by Chocolate, for dessert. He offers it to Briscoe.
"No thanks, I'm driving."
Lololololol.
Also, one that's not funny, but awesome Lennie the cops have j5b4ust opened a truck that turns out to be full of women human slaves/refugees from Asia. He grabs the guy whose truck it is by the collar, and with extreme loathing and disgust throws him back away, saying, "Do me a favor TRY TO RUN!" That was in TNT's Law & Order commercials for a long time.