Tools of Characterization
Characterization in Star Trek III: The Search for Spock
Actions
Actions speak louder than words, and it doesn't matter if those words are in Vulcan, Klingon, or human-speak. They are also our best clues toward characterization in The Search for Spock.
Kirk's willingness to steal the Enterprise despite orders not to demonstrates how far he is willing to go to save Spock's soul. This action shows us where Kirk's loyalty lies (friends over duty and country) and that he'll do what he believes is right.
Kruge's actions also show us exactly who he is even in his first scene. After receiving the Genesis information, he learns his spy and lover, Valkris, has seen it. Deciding this jeopardizes his mission, he destroys the ship she's on without a second thought. Rather than be depressed over this, his next act is to remind the gunner to feed his dog. Based on these actions, we can surmise that he's not a nice guy…and we would be correct.
At least he loves his dog, though?
Clothing
They say you can tell a lot about a person by the clothes they wear. If that's the case, then what does bombasting say about the Elizabethans? We're seriously asking here.
Putting aside the Elizabethans (for now), clothes do a lot of characterization heavy-lifting in the Star Trek universe. Kruge's attire has armor-like qualities to it. It sports a spine guard and large shoulder pads and is colored with browns, blacks and gun-metal greys. Just a glance at his fashion sense tells you he's a brutal and bellicose character who'll kill someone just to prove a point.
That, or he's just so metal.
On the other hand, Vulcan characters prefer flowing robes embroidered with intricate designs and this is appropriate given the film's emphasis on the mystic qualities of their culture. Saavik's the exception. Since her role is as a science officer, we see her in her in Starfleet attire. Also, let's not forget the pure white robes Spock dons at the film's conclusion. Christ Figure, anyone?
As for Kirk and his crew, we see them wearing their civilian clothes far more often in The Search for Spock than in the previous two films. As a result, we get a sense of their more individual styles as people rather than as officers in Starfleet.
For example, based on his open-sleeve leather jacket, we can assume Sulu is a man with no fear of public ridicule. (Of course he's not: did you see his fighting skills? Don't call him "tiny.")
Even less appropriate might be Kirk's personal fashion choices. Pleated mauve undershirt with flared sleeves? Is this really the best the future has to offer?
While the fashion may not be appropriate, the civilian clothes are, as they emphasize the crew putting their personal feelings for Spock ahead of the rank and order of the Federation. On the other hand, characters that follow rank and order, such as Admiral Marrow and Captain Styles, are seen exclusively in Starfleet uniform.
Type of Being
Star Trek has always imbued its alien cultures with overarching traits. The Vulcans prize logic over emotion while Klingons are all about honor and the glory of the battlefield. Humans are curious, industrious, and courageous in the face of adventure and the unknown.
Characters mostly adhere to the traits of their respective species. Saavik is cool and logical even when facing Kruge and the dying Genesis planet. Kruge is all about fighting and honor and the glory for the Klingon race—or a glorious death in a pinch. Kirk and his crew are willing to leap head first into the unknown to save Spock.
But this isn't always true, and there are times when individual personalities play against the established norms of their species. Sarek's a Vulcan, but by his own admission, he has trouble being logical when his son is concerned. Admiral Morrow and Captain Esteban are neither curious nor adventurous, choosing to play things safety and by the book.
So the type of being can be useful for determining character but it isn't a hard and fast rule. The Search for Spock treats its characters like individuals, allowing them to express some traits common of the species they belong to while giving them the freedom to be themselves.
Except for Klingons. We're sure there is a Klingon that's more into writing sonnets than cracking skulls…but he's not in this movie.