Spenser/YMMV

Acceptable Ethnic Targets: Spenser and Hawk have a long-running penchant for making fun of one another's ethnicity, with Susan, a self-described "Jewess from Swampscott Massachusetts," periodically getting in on the action (and making her and Spenser an example of Irishman and a Jew). Any friend of Spenser's who has a sense of humor is equally likely to mock and be mocked in turn, particularly Chollo.
Broken Base: Spenser's fanbase skews older, so there isn't a great deal of discussion of it online. That said, many readers are vocally annoyed by Susan Silverman.
Canon Sue: Arguably averted, although it's a common criticism leveled against the series. Spenser was more prone to making serious mistakes or getting badly injured in earlier books, but after Susan permanently returns to the series post-A Catskill Eagle, Spenser becomes increasingly less capable of error. He still screws up often enough that he's not quite there, and it helps that he usually has no goddamn idea what he's doing for most of a book, and usually just keeps talking to people and turning over rocks until he happens across the right information. Most of the time, Spenser's mistakes have the most far-reaching consequences to people other than himself.
Fan Discontinuity: It is a common opinion that after a certain point, Parker went on creative autopilot and the books began to suffer for it. Where that point is, on the other hand, is a subject of some debate. Rough Weather and The Professional, the last two novels before Parker's death, are widely considered to be the series's nadir, but some fans will place the point of no return - the point where a fan would perhaps do better to pretend that the books ended before then - as early as Chance.
True Art Is Incomprehensible: The play "Handy Dandy" featured in Walking Shadow is apparently extremely confusing and obtuse, and when interviewing the playwright Leonard O (who proves to be an enormous snob) about the case, Spenser lampshades it to hell and back and manages to catch O off guard when he points out that he stole the Tiresias stuff from Eliot. O insists it was a "homage" but Spenser isn't fooled.