Younger than They Look: Danny Glover was only 40 years old when he filmed the first movie despite supposedly being "too old for this shit". Murtaugh was written as an older character (50 in the first movie).
Evil Counterpart: Like Riggs, he was an incredibly tough cop who bent the rules and got results, and they have many of the same snarky personality quirks. He's essentially a dark "what-if" version of who and what Riggs might've become if he'd continued down the self-destructive path he was on after Vicky died. Naturally, he and Riggs hate each other immediately.
Badass: Probably the most Badass character in the entire series. He takes on Riggs and Murtaugh at the same time, twice, and both times he kicks their asses- the first time, effortlessly; the second, he wants them to suffer, but even though he dies he still nearly kills both of them with his bare hands (literally) and after the fight both characters are in crutches.
He kicks the ass of many other characters in the film as well. He also takes Rigg's gun apart in one swift move with one-hand, and at one point he actually dodges a bullet.
Big Brother Instinct: Inverted; he spends the whole film working to buy the release of his older brother, then tries to avenge him once Riggs and Murtaugh kill him.