Gaby's odd behavior throughout most of the film (her occasional recklessness, cool nature in dangerous situations, desire to get drunk and slap around Illya, and occasionally just plain weird behavior) make perfect sense when you find out that she's a British asset and agent working for Waverly who just had her cover blown by two different versions of The Ace from both the United States and Soviet Union, neither of whom knows about her actual affiliation, and dragged into someone else's operation. Considering just now chaotic, dangerous, and tenuous that situation is, it's no wonder she doesn't give a damn.
When Waverly mentions that Kuryakin was already exposed by the time Gaby betrayed him and Solo, he was referring to the Count Lippi incident at the party. So Gaby decided to give him a head start so he would have time to escape, and a chance to save Napoleon and possibly herself. And how did she know he would be able to pull this off? Because he had told her the night before that he kept bugs and trackers on Napoleon. And she somehow deduced that he must have done the same to her as well.
We're told that Uncle Rudi is Gaby's maternal uncle, making him and her father brothers-in-law. And it's blink-and-you-miss-it, but Rudi's last name has a von in it, which indicates that side of the family is of aristocratic origin. This puts an additional classicist meaning on his talk about having "the blood of a racehorse" when looking down on Ilya, as Ilya is both Slavic and of low birth.
Meta-example here in the characterization of Napoleon Solo: yes, it's true that this Napoleon is a good deal more amoral and cynical than his TV counterpart. However, in his last-minute action of giving Illya his father's watch and then quickly making up with him, we can see a bit of the idealism and optimism from Robert Vaughn's portrayal of the character. Perhaps he'll either get a chance to develop a bit more of it assuming there are more movies, or it's already there, just buried a bit deeper under the surface.
A small one: Napoleon crashed the truck into the water to save Illya, instead of just jumping in after him, so that he could use the headlights to look for his body in the water.
Victoria Vinciguerra practically relishes the idea of watching Napoleon suffer, and is disappointed that she can't stay and watch. It's clear that she's worked with Rudi before and admires his work (saying that he's "never in a rush" and describing his torture as "the work of a tireless artist"). Just how many people has Rudi tortured for Victoria? And was it to extract information, or just to satisfy Victoria's sadism?
This iteration of Napoleon Solo is much darker than the series. Solo is a good guy, in the sense that he's fighting on the right side, he clearly knows right from wrong and he knows who the Good and Bad guys are. But as a person he ticks a few boxes for psychopathy. He is at the very least....very very amoral. He's completely detached and cold blooded when he thinks he's killed Illya during their first encounter. His decision to save Illya at the power station looks to stem from pragmatic awareness their mission will be blown if Illya is caught or killed. When he first meets Illya properly, they fight and Illya wipes the floor with him, nearly choking him to death before they're called off each other. Moments later, Solo gleefully provokes Illya into a physical rage despite now being fully aware Illya can take him in a physical fight. We see repeatedly that while he's more than physically capable and a master lock pick, his real skill set lays in manipulation. Even his decision to retrieve Illya's watch and return it just when Illya might kill him could be viewed as less heart warming than manipulative and calculating.
