You might feel you’ve stumbled onto an extended episode of one of Shonda Rhimes’s ABC potboiler melodramas when you watch “Miss Sloane,” a slick but superficial tale of crooked politicians and scheming lobbyists in Washington. Jessica Chastain, channeling tough forties stars like Joan Crawford and Bette Davis, plows aggressively through the title role, but her charisma isn’t enough to rescue a script that’s far less knowing and clever than it thinks it is—not to mention a lot more shallow and implausible.

Elizabeth Sloane is introduced as a top player at the D.C. lobbying firm headed by George Dupont (Sam Waterston), engaged—along with her brood of young aides—in some apparently shady business for the Indonesian government. When approached to take on the task of leading opposition to a proposed bill that would expand background checks on gun purchases, however, she not only demurs but is induced to leave her current job and join the idealistic bunch leading the fight for the bill’s approval headed by Rodolfo Schmidt (Mark Strong), taking most of her staff along with her.

Sloane is a woman driven to win, and it’s unclear whether her defection to the other side is motivated by principle to a cause or merely by the urge to best her old colleagues, not just Dupont but his chief lieutenant Pat Connors (Michael Stuhlbarg). They’re as intent on keeping her from attracting the sixty senators she’ll need to end cloture as she is at getting them, and both sides will resort to any tactics, however underhanded or even illegal, to achieve their end.

Sloane’s task is made all the more difficult by her own personal demons—not only her past habit of cutting ethical corners, which the assistant she left behind, mousy Jane Molloy (Alison Pill), can help Dupont and Connors capitalize on, but her frequenting of an escort service that has brought her into contact with a handsome stud named Forde (Jake Lacy), as well as a dependence on prescription drugs. They will all play into the final thrust of her opponents in the gun law fight—engineering a congressional investigation of her by pliable Senator Sperling (John Lithgow), ostensibly a model of probity. (Of course, logically her old employers would suffer too if her tactics were exposed—she was working for them, after all—but the screenplay is less concerned with logic than the kinds of Machiavellian shifts that mark page-turning thrillers.)

Indeed, Jonathan Perara peppers his script with abrupt twists involving not only Sloane but colleagues at her new firm—Schmidt, Esme Manucharian (Gugu Mbatha-Raw), who has some secrets in her past, and the firm’s exasperated lawyer (David Wilson Barnes)—while the among the opposition Chuck Shamata has a few choice scenes as Sanford, the gun manufacturers’ rep who initiates the entire campaign. If the avalanche of incidents—leading up to a thoroughly preposterous but crowd-pleasing conclusion that recalls Lady Bracknell’s sage observation in “The Importance of Being Earnest” that “The good ended happily and the bad unhappily—that is what fiction means”—had been stretched over a full season of TV episodes, the absurdity of it all would have been much reduced. When jammed into a span of little more than two hours, however, the ability to suspend disbelief collapses as the twists and turns pile up.

Still, “Miss Sloane” remains mildly entertaining hokum dressed up in the trappings of topicality, particularly because the cast, under the characteristically astute direction of veteran John Madden, play it with such relish. Chastain employs a take-no-prisoners approach, uses every trick in her considerable arsenal. She can’t make Sloane sympathetic, but does manage to give her an icy demeanor that exudes confidence and intensity. Of the others Lithgow, Waterston, Stuhlbarg and Shamata positively radiate corruption, while Mbatha-Raw gives Esme some real poignancy—a rarity in an overall cynical piece of work. Strong is surprisingly nondescript as Sloane’s new boss, but Lacy has an easygoing charm as a hustler with a streak of the gentleman to him.

The picture is a gleaming property, with widescreen visuals by cinematographer Sebastian Blenkov that positively glow (a quality well suited to Chastain) and a physical production (designed by Matthew Davies) that prizes elegance. The editing by Alexander Berner manages to juggle all the plot threads reasonably well, and Max Richter’s music is unostentatiously supportive.

As a political commentary, “Miss Sloane” is as subtle as a brick through a window. As a thriller, it has a pulp sensibility that marks it as a B-movie with aspirations. As a character study, it never digs beneath the surface. But while it has absolutely no depth or subtlety, its flashy surface can offer some amusement, though of an instantly forgettable kind.