The action’s hot but the dramatic temperature varies in “The Prosecutor,” a flashy combination of Hong Kong crime story and legal drama starring and directed by Donnie Yen. The veteran action star is convincing and charismatic as a cop who quits the force to become a crusading Department of Justice prosecutor but is let down by a screenplay that’s prone to bouts of melodrama in and out of the courtroom. Entertaining enough despite its flaws, “The Prosecutor” has topped the Hong Kong box office for two weeks (thus far) since opening on Dec. 21 and ought to perform well in limited U.S. theatrical release from Jan. 10.

Containing less action than a regular Donnie Yen film, and with his character delivering lines such as “I’m getting old, I can’t catch thieves anymore” and “I just got old” as a reason for his career change, “The Prosecutor” sparked...