South Park hit it spot on with the manatees and their idea balls. The "jokes" aren't funny, they're interchangeable and have nothing to do with the often half developed (or less) plot, some of their attempts at humor make no sence at all ("like that one time peter went swimming with the cows" heh heh heh *gunshot*). And they don't seem to realize that their pop culture references will become obsolete, making any cheap laughter they may have gotten from a reference meaningless in a few months.
It also seems like the manatees think that random bursts of violence are just hilarious. No setup, no reason for the violence, just randomly smashing someone in the face with a chair. It seems they think its even better if they show violence towards women, animals, or just someone whose plain defenceless. Then there are the tasteless outbursts (I recall one episode where they said people in wheelchairs are monsters). Once again, no setup, no provocation, just tasteless, tactless, offensive shit.
Don't get me wrong, I can laugh my ass off at something incredibly offensive or violent, but the formula is Timing + Violence = Comedy. NOT Violence = Comedy.
Also, I don't dislike the show simply because of the cutaway gags. I'll compare it to Scrubs since both shows use cutaway humor. Scrubs is still funny because the jokes are relevant to whats going on, brought on by a comment or observation. These flashes don't consist of 5 minutes of fighting a chicken for the FIFTIETH FUCKING TIME, but are short, few, and far between. Another thing that sets Scrubs apart from Family Guy is that episodes of Scrubs actually have a plot. The manatees at Family Guy may attempt to scribble a plot, but without the use of their idea balls, whatever they have falls apart to some undeveloped thread of overall pointless events that serves as a break between cutaway jokes. Scrubs is also able to take a more serious tone and have dramatic, touching moments. Perhaps the best example of this in Scrubs is "My Lunch." The episode has a scene where three patients die of rabies contracted from an organ transplant. One of the patients is a good friend of Dr. Cox who feels guilty because he rushed the transplants due to the critical states of the patients. Dr. Cox goes into a self-destructive depression in his guilt ridden state... Maybe I'm going a bit off topic, but you get the point that cutaway humor can work. Family Guy just fails horribly at it.
I will agree, however, that the first three seasons (before the cancellation) were much better than the newer episodes. Those episodes didn't employ as many random jokes. The cutaway gags tended to be short and somewhat related to what was happening. That show should've never been revived.