It is revealed Milhouse is (or was) lactose intolerant. This has also been mentioned in the flashback episode 'Lisa's Sax" in which Milhouse tells Bart that he has to drink soy milk because real cow's milk could kill him.
It's actually lethal if you mix various cleaning solutions into one blend.
Homer shows Marge a picture of him punching former president George Bush, a reference to the seventh season episode "Two Bad Neighbors", and then shows a picture of him punching then current president, George W. Bush. This is the first appearance of George W. Bush and now every living president has made an appearance on the show. The most recent Presidents who have not been shown in animated form are Herbert Hoover.
The opening gag 'I will not leak the plot of the movie' is a reference to the then-upcoming Simpsons movie.
Bart's scheme of painting house numbers on curbs to make money is possibly based on the real childhood of longtime Simpsons writer George Meyer.
Marge's amnesia is neutral as she can remember everything but one person.
The title and episode plot is a reference to the movie Regarding Henry, in which Harrison Ford plays a man with amnesia.
The scene where Marge and Homer go to a wedding uninvited is similar to various scenes from Wedding Crashers.
Homer writes on the sidewalk that the '74 Oakland A's are the best team ever. Soon after, several members of the team drive by and thank Homer for remembering them. Sal Bando and Gene Tenace, two members of the actual team, make cameo appearances.
Marge's amnesia is caused when she passes out and hits her head on a stool, a reference to the film Million Dollar Baby.
Marge's quote, "Et tu Zud?" is reference to 'Et tu Brute,' from Julius Caesar by Shakespeare.
When Ned holds the comics for Bart and the others, the one on top is called Little Jesus, a parody of the Little Lulu comics.
One of the cleaning products Marge used was Mop 'n' Brag, a spoof of the product Mop 'n' Shine.
Homer states that he and Marge first had sex in the "Plywood Castle" at the mini-golf, but an earlier episode shows them in the "Windmill", although they both look similar. However, in the episode where they first do it, Homer (idly) promises Marge he'll buy her a real castle one day.
When Dr. Hibbert is holding up the fingers, the nails are facing away from Marge but in the next scene the nails are facing towards her.
When Marge is having her first speed-date and says "Oh, that's so sad!" a person can be seen behind her, but then she reaches behind her for the air horn.
Marge kicked Homer out of the house but he owns it outright, she has no legal right to live there without him or kick him out.