In "And Maggie Makes Three", a Flashback shows that when Marge got pregnant with Maggie, practically everyone congratulated Homer, and he interpreted all of it to be kudos for landing his dream job at the bowling alley...up to and including Moe's "Hey Homer! Way to get Marge pregnant!" When he gets home, he observes that Marge's friends are throwing her a party, where they're showering her with baby-sized gifts, which he casually shrugs off. At that point, Maude Flanders congratulates Homer on his new job, prompting him to say "New job? MARGE IS PREGNANT?!" and run to the bedroom in a panic.
Similarly, in "Homer's Night Out", while coming home from work people keep greeting him and doing hula dances. He isn't aware that the picture of him dancing with a woman has circulated (despite there being a copy of the picture right behind Apu), and just figures that they're on drugs.
In the episode where Marge stars in a musical version of A Streetcar Named Desire, after she delivers the last line ("I have always depended on the kindness of strangers.") the cast breaks into a musical number about how "You can always depend on the kindness of strangers..."
During the gay parade, Marge hears Patty and Smithers, hidden each in their own closets, proclaiming that they're gay and proud of it. Marge then asks, "Wouldn't it be nice if that man and that woman got together [romantically]?"
"Goodbye Adil! I'll send you those Civil Defence plans you wanted!" - Homer to foreign exchange student Adil in "Crepes Of Wrath", who is not just clearly a spy, but in the process of being deported from the country under espionage charges.
It happens again in the episode mentioned above when Chief Wiggum makes it clear that he won't help him for not bribing him but sarcastically tells him to wait for "Officer Like-I-give-a-damn". Guess what Homer does?
Another Homer example - searching for his half-brother Herbert, Homer asks the Orphanage where he might be. The director tells him that such data is confidential but says that Detroit is a good place to look for him. Homer keeps asking and missing the obvious hints, even bribing the director. The director has to say "He's in Detroit" point-blankly for Homer to get it.
In Homer's Phobia Homer is blissfully unaware that John is gay. Marge attempts to point out this fact when Homer suggests John and his wife come over for dinner, with Homer Comically Missing the Point until she tells him point blank:
Marge: Homer, didn't John seem a little "festive" to you? Homer: Couldn't agree more, happy as a clam. Marge: He prefers the company of men! Homer: Who doesn't? Marge: Homer, listen carefully. John is a Ho - mo... Homer: Right. Marge: ...Sexual! Homer: AAAAHHH!
Also the clerk in the episode "Bart Star" is a subversion: at the end, it's revealed that he only wanted to play a crude joke on Marge:
Marge: He's going to need, uh… you know, protection. Guy: Sure… one helmet coming up. Marge: I was thinking more of… protection… down there. Guy: Oh, why didn't you say so? Knee pads. You got it. Marge:(laughs very nervously) I'm talking about his (quietly) personal area. Guy: Ah ha. Say no more. I read you loud and clear. The old shoulder pads. Marge: (annoyed) Look, I want a cup Guy: Cup, could you spell that? Marge: C - U - P I wanna C - U …oh my god!
In the episode 'Grade School Confidential'
Lisa: I was in the library at the time, but Janey told me Principal Skinner and...what's her name? Bart's teacher? Marge: Mrs. Krabappel? Lisa: Yeah, Krabappel. They were naked in the closet together! Marge: GASP! Oh my goodness! Homer: Wait a minute...Bart's teacher is named Krabappel? I've been calling her Crandall! Why didn't someone tell me? Oh, I've been making an idiot out of myself!
Kinda counts as a double example seeing as how he not only misses the point (teachers making out) but also misses the more obvious mispronunciation of Krabappel.
Mr. Burns got a good one when he was trying to get a biopic of himself made:
Burns: All right, Spielbergo, I want you to do for me what Spielberg did for Schindler. Spielbergo: But, Schindler es bueno! Burns es diablo! Burns: Oh, pish tosh! Oskar Schindler and I are like two peas in a pod! We're both factory owners, we both made [artillery] shells for the Nazis - but mine worked, dammit!
Played with in an early episode, "Fear of Flying". After Homer enters what is clearly a lesbian bar (it's is even called "She-She Lounge" and is filled with stereotypical lesbians):
Homer: Wait a minute... there's something bothering me about this place... I know! This lesbian bar doesn't have a fire exit! Enjoy your death trap, ladies.
In "Much Apu About Nothing" a bear roams the streets. It is caught and Homer immediately demands more protection against bears, even though it was the first time the town ever encountered this problem. After a special "bear patrol" is installed Homer tells Lisa he fails much safer now.
Homer: Not a bear in sight. The Bear Patrol must be working like a charm. Lisa: That's specious reasoning, Dad. Homer: Thank you, dear. Lisa: By your logic I could claim that this rock keeps tigers away. Homer: Oh, how does it work? Lisa: It doesn't work. Homer: Uh-huh. Lisa: It's just a stupid rock. Homer: Uh-huh. Lisa: But I don't see any tigers around, do you? [Homer thinks of this, then pulls out some money] Homer: Lisa, I want to buy your rock. [Lisa refuses at first, then takes the exchange]
In Mayored to the Mob, Homer is convinced that he's killed Mayor Quimby after sending him flying out off a window. When he hears the mayor crying for help and sees him dangling from a window ledge, he exclaims, 'His corpse is climbing the building!'