Dr. Slop is the village doc who's way into his hobby-horse: obstetrics. All righty, then. He possesses the latest and greatest medical equipment, and he's so eager to try it out that he scrapes the skin off of Toby's hands demonstrating how forceps work.
To be honest, Dr. Slop is one of the most unappealing characters in the book. If his name weren't clue enough, he's a "little squat, uncourtly figure … of about four feet and a half perpendicular height, with a breadth of back, and a sesquipedality of belly" (2.9.1). Not only that, he's incompetent. He forgets his instruments, can't get into his bag, breaks Tristram's nose, and gabs away while Tristram is screaming in pain after the accident with the window sash. He's not the guy you want to see at your yearly checkup.
Tristram doesn't spend as much time discussing Dr. Slop's personality as he does some of the other characters in the book, but we can get a pretty good idea what's going on with him by looking at some of his key actions: he has a temper tantrum after falling off his horse, he curses Obadiah, he throws the bandage at Susannah after she burns his wig, and, finally, he gets himself into a "wrath" during a minor debate about virginity.
When you add up all these moments, Dr. Slop turns out to be the opposite of Toby Shandy. He needs to simmer down and stop being a jerk.
Dr. Slop's, er, sloppiness complicates his class position. We're used to thinking of doctors as being near the top of the social hierarchy, but that wasn't always true. Until the late nineteenth century, doctors didn't get much credit, and no wonder—they couldn't do much except bleed people and prescribe useless and often dangerous medicine. Take Mrs. Shandy's reaction to the mention of a C-section: she turns "as pale as ashes at the very mention of it" (2.19.29). There's no scheduling your C-section around a Hawaiian vacation in the eighteenth century. Doctors were pretty much butchers, just a little above servants in the social hierarchy.
Where does that put Slop? We know he's just a little above a servant because he tussles with the servants like an MMA fighter and hangs out in the kitchen. Susannah even sets fire to Dr. Slop's "somewhat bushy and unctuous" wig—rather obtrusive and oily, just like Dr. Slop himself (5.3.4). Mr. Shandy refuses to let Dr. Slop work in the parlor, ordering "If Dr. Slop has any drugs to pound, let him do it in the kitchen" (3.22.6) (Check out the section on "Corporal Trim" for more about the upstairs/ downstairs split.)
Dr. Slop got some country in him, but he can also tango with the upper classes. From our twenty-first century perspective, we can point to Dr. Slop as evidence of a new upward mobility. Throughout the late eighteenth and then all through the nineteenth century, a middle class slowly emerged in England that was made up of people like Dr. Slop—not peasants or servants, but not quite the gentry, either. We've got a term for that: new money.