Floyd Thursby was Brigid's partner, but he winds up dead before we ever get to meet him. We learn from Tom Polhaus that several years ago, Thursby was a St Louis gunman who got in trouble with the law several times for petty crime and battery charges. He got mixed up in the mob scene when he became the bodyguard for mob boss Dixie Monahan. But when Dixie had to go into hiding after being unable to pay off his debts, Thursby also fell off the radar. No one knows how he ended up in Constantinople, working for Gutman. Brigid explains that she and Thursby worked together to steal the falcon and run off without giving it to Gutman. At the end of the novel, we learn that Brigid killed Archer in an attempt to frame Thursby for Archer's death. But she wasn't expecting for Thursby to then be killed by Wilmer.
Sergeant Tom Polhaus is a detective and seems to be mostly on Spade's side. Despite having to grill Spade a few times over the course of the novel (Spade is the #1 suspect on their list of possible suspects for Archer's murder), Tom is on good terms with the PI. The two occasionally have lunch together, and Tom lets Spade in on the news the police had gathered about Thursby. Even though Spade has a general mistrust of the police, he has a good opinion of Tom and considers him an honest cop.
Dundy is a lieutenant in the police department and represents all the things that Spade hates about cops: he's self-important, inefficient, and condescending. Dundy is an arrogant bully who likes to push people around. He grills Spade on several occasions, constantly threatening to lock Spade up. But Spade knows that Dundy has no evidence linking him to Archer's death, and that these empty threats are merely an attempt to shake him up.
Rhea Gutman is one seriously mysterious character.
She's Casper's daughter and appears for a very brief scene, in which she is drugged and barely conscious. She had been using a small pin to scratch her stomach to keep her awake until Spade came. She begs him to help Brigid, but not to tell her father about it or else he'd kill her. She explains that Cairo and Wilmer have taken Brigid to an abandoned house, but when Spade gets there, the house looks as if it hadn't been occupied in weeks. When Spade returns to the hotel, Rhea has disappeared without a trace.
Did Casper set up his own daughter to outsmart Spade? We never find out what happens to Rhea, but it's possible that Casper may have killed her. Tom reports to Spade at the end of the novel that Wilmer shot and killed Gutman, but there is no mention of Rhea at all. This is one mystery that will remain unresolved.
Jacobi is the captain of the ship La Paloma, which arrived in San Francisco from Hong Kong.We learn from Brigid that she partnered up with Jacobi to bring falcon from Egypt to San Francisco. Jacobi is killed by Wilmer, but manages to bring the falcon to Spade.
Luke is the house-detective at Cairo's hotel, the Belvedere. He helps Spade a few times when Spade needs the inside scoop on Joel Cairo's comings and goings. Luke is an honest, straightforward guy, who is willing to give Spade inside information, as long as Spade doesn't lie about why he needs the info.
Sid Wise is Spade's lawyer, and seems to be pretty honest, as lawyers go. Spade advises Iva Archer to pay a visit to Wise in order to explain where she was on the night of her husband's murder. When Spade goes to Wise to see what Iva told him, Wise fills Spade in on the details, without holding back any information. It's clear that Spade trusts Wise, which isn't something that we can say often when it comes to Spade.
DA Bryan represents the kind of corrupt institutional official who has let too much power get to his head. Bryan bullies and threatens Spade even though there is no evidence pointing to Spade as either Archer's or Thursby's killer. Bryan's a manipulative, power-hungry man, who seems less interested in finding out the truth than in imposing his authority on others. Spade of course doesn't put up with Bryan's empty threats, and we wouldn't either if we were him.
Kemidov is a Russian general who lives in a Constantinople suburb. We never met Kemidov in person, and only hear about him through Brigid and Gutman. According to Gutman, the Maltese falcon had made its way into Kemidov's possession, but Kemidov had no idea about the bird's real worth. But when Gutman made him an offer to buy it, Kemidov turned it down. Gutman wasn't sure whether his over-eagerness tipped Kemidov off to the bird's value, but Gutman couldn't take the risk so he sent Cairo, Brigid, and Thursby off to steal the bird.
In the end, we find out that Kemidov did in fact figure out the true history behind the Maltese falcon, so before Gutman's crew stole the bird, Kemidov had already replaced the real bird with a fake one. It appears that Kemidov has the last laugh.