I can't really think of anything that physically disgusted me on Family Guy, or on any cartoon for that matter (not even the 'Pube Fair/ Scott Tenerman' episode of South Park), probably because I know it's not real. IF the same type of stuff happened (mainly the Family Guy 'Vomit scene' or 'cat shaving' scene) in a live action show or real life, than I'd find it disgusting.
For the most tasteless joke/bit from Family Guy when Peter and Brian went back in time to the 80's. Brian was hitting on some girl when her boyfriend "Quintessential 80's guy" got pissed and tried to pick a fight with Brian ( "Any time, any where!). Brian says to meet him on top of the World Trade Center the morning of September 11th 2001.
For the most tasteless joke/bit from Family Guy when Peter and Brian went back in time to the 80's. Brian was hitting on some girl when her boyfriend "Quintessential 80's guy" got pissed and tried to pick a fight with Brian ( "Any time, any where!). Brian says to meet him on top of the World Trade Center the morning of September 11th 2001.