Who: Yukari
Flaw: Yukari is a misunderstood troll who does so for her own amusement.
Why She is Misunderstood: She's doing it because as the sage of the youkai, she has a reputation to uphold. People are supposed to fear youkai, and yet Yukari can't bring herself to attack humans (not without reason, at least). Thus, Yukari needs to find an alternative way to make sure she's the most feared youkai in Gensokyo, and this takes the form of trolling people to the extreme. So far, as Reimu has stated she's the worst youkai in Gensokyo, it seems to be effective. This is also why she keeps her more altruistic actions a secret, to the point of actively keeping them out of history's records.
....that and she's doing it for her own amusement.
I can say a lot about Tenshi and Kaguya, and to some extent, Meiling. Those three are easily the characters in the series that got twisted the most by fandom.
Tenshi
Flaw: Masochist
Why she's misunderstood: "Punish me" DOES NOT means asking to get beaten up. Villains taunting heroes/heroines to defeat them is something very common in medias. That phrase is nothing more than a taunt in order to start a fight.
I think this subconciously came about because Tenshi said it so often, as other characters have said the equivalent of "Punish me!" yet it hasn't been picked up. Of course, there's a logical reason why Tenshi said it so often. She instigated the entire incident in the first place to get people to fight her (unlike every other incident in the series, where there's been some other motive). Fandom seems to have ignored that though, but this is also due to Tenshi never having any further storyline roles ANYWHERE to show her other aspects of her personality that she presumably has (despite quite a bit of foreshadowing in some SWR endings that she might have an even more serious motive she's keeping hidden, sadly)
Kaguya
Flaw: NEET, obsessed with TVs, video games, and computers, and lazy
Why she's misunderstood: What is this I don't...?! I'm really baffled on how fandom turned her into a NEET. Just because she hides out in Eientei to avoid the Lunarians does not mean she's an indoor-type. Inaba of the Moon and Inaba of the Earth shows that she's more or less the exact opposite, what with wanting to hold moon festivals and going outside to perform certain activities. Being lazy is greatly exaggerated as well; she's not that lazy in canon.
It's actually been the opposite as early as Bohemian Archive in Japanese Red. It was Kaguya's idea to set up the Lunar Expo, after all.
I think this came about because, before BAiJR came out, there was very little characterization for Kaguya, so the fandom made their own conclusions and it was too late by the time her characterization was further displayed in official sources (that and people tend to ignore many further official sources in fandom, anyways). She has very few lines of dialogue in IN, including the endings. Admittingly, even the endings imply the opposite from what little can be gleamed from them. Of course, considering that fans don't post endings and it's very hard for the average human being to see an ending in the first place, well....
Meiling
Flaw: Falls asleep often and does her job badly
Why she's misunderstood: She takes siestas, not falling asleep all the time, and she instantly wakes up if intruders shows up. If she really is incompetent, then Remilia would have fired her since a long time ago.
I think the whole "Siesta" thing was a joke that Akyuu thinks she's taking a siesta, but she's actually falling asleep (then again, maybe not, considering it's a scheduled thing at Noon).
Her article in BAiJR does have her give a suspiciously specific denial that she wasn't sleeping, though.
I could be wrong though. It doesn't particularly matter much to me (though both are funny jokes if I'm right, IMHO)
Hisoutensoku's confirmed that at least some of the sleeping on the job is canon, however.
None of that confirms or denies that she does her job badly. Me personally, I think she does a decent job at it (she's on the lookout the times she's shown in Oriental Sacred Place) but that the task is simply too daunting to expect too much of her. After all, she's required to do her job 24/7 without any breaks and her BAiJR article implies that the SDM garden is pretty friggin' huge (it looks huge in Oriental Sacred Place the few times it's shown, too) in a world where everyone can fly.
Of the people known to break into the mansion, most of them were the insanely powerful types or insanely sneaking types to begin with (Marisa, Yukari, Eirin, and um... Alice, I guess, etc. Well, ZUN said she's basically Youkai Marisa)
Remilia's probably aware that the task is too daunting for her but doesn't care because it's A) funny (BAiJR implies that Remilia does this sort of thing to Meiling often), and B) not too big a deal.