Six years ago I could say I was a fan of the series. I found the humor to be more subtle and tasteful than what you'd expect from South Park. But as the seasons rolled on things became more unbearable to the point that I can't even watch the show anymore without seeing wasted opportunities and shock value humor.
One thing that stands out in the early seasons was the line from the opening song "Those good old fashioned values." This rings true when you see that much of what Peter did was for the sake of his family. The well-fare fraud, trying to make Chris Jewish, "acquiring the assistance" of the Pope to talk to his father.
Now adays the entire cast has become a relentless bunch of sociopaths who don't care who they abuse. Even Lois, who went to such lengths to give her daughter a decent spring break, became someone cold enough to tell her daughter to kill herself. The woman Peter fought so hard to win over has expressly stated that if he were unable to move, she would leave him.
Brian and Stewie taking up much of the show's airtime becomes a minor offense when the two prove to be more moral and like-able than Peter or Lois. When they're together anyway. Plots that center around Brian and whatever political debate or love interest he's trying to win get stale fast though.
In the early seasons much of the humor was derived from early pop-culture references and various randomness. Even without understanding those references there are plenty of moments that made me laugh. Modern episodes seem to have jumped on this mentality that being as offensive as possible is what's funny, so every episode we're treated to a joke about the big "hot buttons" of offensiveness. Those being rape, abortion and 9/11. Gross-out humor has also reached a peak where even the most desensitized can't enjoy a pizza while watching what was once their favorite show.
Laziness in writing is another recent fault, to the point that the show spends much of it's time looking for ways to parody or lampshade itself, rather than work things into the plot with any decent level of writing ability. I know it's a gag show, but you can tell they've stopped trying when they call attention to the fact that something doesn't make sense, and just disregard it on the grounds that no one would care because status quo is god.