UGARTE: You know, Rick, I have many friends in Casablanca, but somehow, just because you despise me you're the only one I trust.
All right, so sounds like a bit of a backhanded compliment. But really, this is Ugarte's way of saying that everyone in Casablanca is totally fake, greeting you with a smile when they're actually ready to either rob you blind or throw you in prison. Because Rick openly hates on him, he figures he's got to be a good guy.
RENAULT: Because, my dear Ricky, I suspect that under that cynical shell you're at heart a sentimentalist.
Here's another instance where a line could be perceived as not exactly a compliment. Renault doesn't strike us as the biggest sentimentalist, so calling someone else that may not be the highest form of praise. But when Strasser's killed and Renault immediately changes his stripes, we realize he might actually have been expressing his admiration for Rick after all.
RENAULT: Well, Mademoiselle, he's the kind of a man that, well, if I were a woman and I were not around, I should be in love with Rick.
No greater way of saying you admire somebody than confessing you wouldn't mind seven minutes in Heaven with 'em at a slumber party.
SACHA: Boss, you've done a beautiful thing.
This line is in response to Sacha, the bartender, finding out that Rick has rigged the roulette wheel to help out a couple in distress. You get a real sense that any of Rick's employees would take a bullet for this guy. He must be awfully generous with the Christmas bonuses.
RICK: Louis, I think this is the beginning of a beautiful friendship.
Rick and Renault have sort of quasi-admired one another via some thinly veiled antagonism for much of the movie, but now that Strasser's out of the picture (Rick doing Renault a favor) and Renault not giving Rick up (Renault doing Rick a favor), the two men are free to express their mutual respect a little more openly. We see many friendly tennis matches in their future.