Amnesia Missed a Spot

Uh-oh. The Masquerade that you've worked so hard to build and maintain has suddenly been broken. Now a bunch of Muggles know that you and your entire family are vampires/werewolves/witches/what-have-you. But no problem. All you've got to do is whip up some mojo and give them a handy case of Laser-Guided Amnesia, right?

Well, no. See, turns out your spell/hypnosis/whatever, didn't work the way you'd intended. Sure, maybe it wiped the memory of a few, but there was this one guy whose memory remained intact. (Probably The Hero or someone close to him, but most certainly a character who has relevance to the plot. This trope is not wasted on minor characters.) For another a variation, the character in question may have their memory mostly wiped, but retain some crucial piece of information relating to The Masquerade. (Which they may not immediately recognize the significance of.)

Fake Memories usually have similar problems, someone always finds the holes.

Compare Ripple-Effect-Proof Memory, which may overlap, and Glamour Failure. Contrast Laser-Guided Amnesia, which is when the mojo works.

Examples of Amnesia Missed a Spot include:

Anime And Manga

In RahXephon, the Mulian mind control is shown to be imperfect when Hiroko realizes she has forgotten something really important when she meets Ayato again after his disappearance.
Some of the girls from The World God Only Knows remember stuff after Elsie erases their memories. They usually come up with their own version of what happened to explain. This is explicitly because New Hell has power issues, and only erases the absolute minimum. This can bite Keima in the ass; for example, he took a girl to an amusement park for a date, which ended in a kiss. According to her memories, he ditched her halfway through for no reason whatsoever.
When Albert Maverick Unpersons Kotetsu before framing him for murder in the 20th episode of Tiger and Bunny he slips up and misses mind-wiping two crucial individuals, Kotetsu's former boss Ben Jackson and judge Yuri Petrov/vigilante Lunatic. Both turn out to be vital in helping Kotetsu avoid capture by his former friends.

Comic Books

The ending of Crisis on Infinite Earths shows that only the Psycho-Pirate remembers the multiverse or the details of the Crisis itself. Everyone else only has vague memories of a big battle and the skies turning red.

Film

Men in Black: When J meets Dr. Weaver in the Morgue, they vaguely notice that they may have met before, but dismiss it as Deja Vu. In the beginning of the movie, they had met, but K had wiped both of their memories.
X Men First Class: At the end, Xavier (at least apparently) wipes MacTaggert's memory to keep the mutants safe from the CIA. All MacTaggert remembers is a few glimpses of leaves and Xavier kissing her.

Literature

Happens in The Heroes of Olympus by Rick Riordan. except It was intentional.
Mind-wiping in Artemis Fowl leaves "residual memories" which can be used to trigger total recall.
In Matched by Ally Condie, witnesses to an event are ordered to take a mind-wiping pill, but the main character only pretends to and keeps her memory.
In Graveminder, Amity keeps a notebook to try to get around the town's magical amnesia. It is suggested, however, that she has trouble remembering to check the notebook.

Live Action TV

Coincides with Ripple-Effect-Proof Memory in The 4400. The people who originally took the 4400 come back and capture a large number of 4400 children, stating that the future has not been changed as they had hoped and that they must place these children into new parts of history so that they can alter the future. One of them, Maya Skouris is wiped from all memory, with the exception of Agent Tom Baldwin, who continually sees her when his wife Alanna uses her powers on him. (She can psychically construct alternate realities for people.) He doesn't recognize Maya, but Alanna says that he must know who she is, since the alternate realities are created out of the subject's memories.
This kicks off the main plot of the Star Trek: The Next Generation episode "Who Watches The Watchers"
Twice on No Ordinary Family with the same characters.

1. Daphne uses her newfound idea push powers to tell her inquisitive boyfriend not to ask about the family's special abilities. It works, but then a few hours later he broaches the topic again. So she pushes again, which works for a few hours again. Etc. She finally ends up telling him.
2. Jim convinces Daphne to mind-wipe BF of his knowing about the family, so she gives him the instruction to "forget about when you learned I was special." This time it works too well, as he forgets their entire relationship.

The memory drug in Torchwood, called 'Retcon', can sometimes leave nagging little details in the victim's mind. If they're distanced from all the weird things they've seen, it won't be a problem, but if something triggers it the memories come back. This is how Gwen re-learns of Torchwood in the pilot after Jack wipes her mind.

Video Games

In Persona 3, ordinary people who don't experience the Dark Hour have their memories revised afterwards to explain anything strange that occurs during the Dark Hour. (Which they might notice after it passes). In one scene, Mitsuru mentions that so many people are coming down with Apathy Syndrome that the memory revision can't keep up.
- At the end of the game, either the protagonists (in the bad ending) or the entire world and the protagonists (in the good ending) have their experiences of the Dark Hour, as well as all the bonds of friendship and Character Development that occurred because of it, erased from their memories. Everyone, that is, except for Aigis, who explicitly remembers everything. Depending on which ending it is, the character's situation is either wistful or downright Fridge Horror, because in the bad ending she knows that The End of the World as We Know It is hours away from happening but there's absolutely nothing she can do to stop it, and she can't even tell her former friends about it because they don't even remember who she is.
- It's also implied to have missed to the Main Character in the good ending, since he/she can speak to Aigis about it in the last two days before graduation. However, since the narrative skips from the aftermath of the Final Battle to the day before graduation, it's ambiguous whether he/she retained all memories along with Aigis and simply kept quiet about it for three months, or whether the memories came back on that specific day.
The first Knights of the Old Republic had this as the backbone of the plot. Revan's fragmented memories, as spied on through Bastila via the Force Bond were supposed to lead the Jedi to the Star Forge with your Player Character being none the wiser.

Western Animation

In X-Men: Evolution, an entire sports stadium of people learn about the different mutants among them and their powers. To maintain their secret identities, Professor X tries to erase everyone's memory of the night, but blacks out before he can finish erasing Principal Kelly's mind. Principal Kelly later goes on to be very anti-mutant. The episode in question can be seen here.