Tacky cattiness at the expense of plot

The show: Family Guy, once a paragon of animated freshness compared to the stale Simpsons, now degenerated to a platform for offensive jokes for the sake of being offensive, simultaneously tacky and catty attacks on celebrities, and a complete disregard for both inter- and intra-episode continuity.
The episode: "Big Man on Hippocampus," first aired back in January and rerun recently.
What happened: Taking a page from The Simpsons, the writers set up the main story of Peter's amnesia with a seemingly unrelated first act in which the Griffins go on Family Feud. During taping, Peter has an accident and loses his memory. The family tries to restore his memory with some old family videos, but Peter is more interested in watching Pretty Woman. That night, Peter spies on Lois undressing, and Lois re-introduces Peter to sex. The next day, Peter decides that despite how much he enjoyed sex with Lois, he'd rather have sex with other women. That night he brings Tiffani-Amber Thiessen home with every intention of having sex with her. Lois leaves in a huff. Peter asks Tiffani about her necklace. "Is that how you spend your Saved by the Bell money?" Peter asks.
What doesn't make sense: So when did Peter relearn what Saved by the Bell is? And why would he know about that teen comedy but not remember how to drive? So basically, Peter's amnesia is suspended just long enough for him to make a tacky, catty remark to a celebrity. Do the writers feel proud of themselves here? Worse, this is one of those nits that could've been prevented with a simple line of dialogue inserted earlier: besides Pretty Woman, the box of videotapes could have also have had a Saved by the Bell tape. It wouldn't have been necessary to actually show Peter watching that show, but just to mention it eliminates this nit free and clear.
One more thing: Yes, I'm still watching this on FOX. Supposedly the jokes are funnier on Adult Swim. Why? Because they can use all the swear words and racial slurs they want? Hey, look at me, I find humor in the prevalence of racism in this country! Give me a break. Besides, bleeps can be exploited for humor much funnier than any catty stereotype that could air on Adult Swim; this is something which this show has actually done in the past. In my opinion, this bit from "PTV" is the funniest in all of post-cancellation Family Guy:

"You know, you're lucky you're good at (bleep) my (bleep) or I'd never put up with you. You know what I'm talking about, when you (bleep) a lubed up (bleep) of toothpaste in my (bleep) while you (bleep) on a cherry (bleep) Episcopalian (bleep) extension cord (bleep) wetness (bleep) with a parking ticket. That is the best." — Peter Griffin