Have you ever described a girl with the phrase, "What a magnificent body! Shouldn't I like to see it on the dissecting-table" (15.17)? Yeah, we haven't either. Yet this is how Bazarov first speaks of Madame Odintsov. On the one hand, he acts like a typical guy, instantly drawn in by Odintsov's good looks. On the other, there's something strange going on here. Even in his compliments, he keeps up a distance from Odintsov, a distance not so different from that between a doctor and his patient (or, to use an ickier word, specimen).
What is clear, though, is that Bazarov is a cad and a womanizer. Initially, he imagines that Odintsov will be an easy sexual conquest, and he becomes frustrated when all those mushy things like feelings start to enter the equation. When she shoots him down, he takes all of that sexual energy and re-directs it at Fenichka. Bazarov's a lonely guy, but he tries to conceal this from himself by focusing on women as sexual objects (not that he has much success here either).
The only other bit of scandal that enters in comes early on when Nikolai admits that he has taken Fenichka in to live with him. If you miss it the first time, it's pretty clear that he's been sleeping with her when you learn that the two of them have had a son together, little Mitya. Today, this probably doesn't seem like much, but at the time it might have been a cause of great embarrassment since Nikolai is the master and he's begun sleeping with his servant.