Take L: is he a borderline-sociopathic Knight Templarscarcely any better than Light, an Anti-Hero whose methods are questionable but who is not really evilper se, or just an endearingly socially inept genius with a difficult past who has had lifelong problems fitting in? Word of God calls him 'slightly evil', which seems to fit in best with the second interpretation, but even that's probably up for debate. Then you have the much-debated question of whether L and/or Near have some form of autism. You decide.
Near and Mello both get it, also. Is Near an albino? Does Near dislike L? Does he hate Mello, does he secretly feel friendship for him, is there massive amounts of Ho Yay involved? Is Mello Catholic, or is there some other reason he'd wear a rosary? Is Mello an Anti-Hero or an anti-villain? Is Mello a super-temperamental guy, or is it just that Near pushes his Berserk Button? A fanfic claimed that Mello was faking his insanity to throw Near off. And then there's Matt, who didn't even have that much of a personality, so that subject is pretty open. About the only things consistent are the fact that he's a techie who likes games and he's pretty lazy. Then you get into Misa, Ryuuk, Mikami, even Takada.... Death Note has massive amounts of this sort of thing.
There's also the endless debate over whether or not Matsuda's speculation that Near used the Death Note to restrict Mikami's actions is true, though this theory works less for the anime than it does the manga; in the anime, Mikami commits suicide during the final confrontation, while in the manga, he inexplicably dies some time afterwards, which Matsuda considers possible proof that he was written into the Death Note. Word of God also mentions that Near "cheats."
There's also Misa Amane. Is she just a naive young woman whose traumatic past lead her to idolize the one person in her life whom she percieved as being on the side of justice and righteousness (regardless of whether he actually was), an emotionally disturbed woman-child who is unable to comprehend the notion that human life has any value other than fulfilling her own hedonistic desires, or a nihilistic sociopath who casually declares the act of tricking someone into loving you so much that they would lay down their life for you "a beautiful way to kill?" The series itself can support any interpretation.
One common Alternative Character Interpreation for any Death Note user is whether or not it's the power over life and death bringing out their darker side, or if just using a Death Note will drive a human absolutely batshit insane. There is a marked difference in Misa, Light, and Mikami's mental stability and personality depending on whether or not they have a Death Note at the moment. As such, Misa can be argued to fit the first interpretation when she's in her right mind, and the second when she's in her "2nd Kira" persona.
The shinigami's are questionable in some cases, specifically Rem: is Rem a good shinigami looking out for a human she/he fell in love with, or is she/he still a monster that survives by killing? Also, are any shinigami's evil, in that they were made to kill people therefore are only fullfilling their nature?
Taro Kagami from the pilot chapter. Throughout the story, he comes across as a genuinely good kid who simply got thrown into horrifying circumstances way beyond his control. The pilot's ending, however, is very open-ended. We know Taro kept the Death Note. It's unclear whether he simply kept it or if he did a Face-Heel Turn and started using it again. Unlike Light, whom Word of God specifically identifies as "evil," Taro is someone whose moral alignment is genuinely open to interpretation.
Also, anyone in the main story. Is Light a psychopathic depraved lunatic with delusions of godhood who kills people indiscriminately for a reason which has been inherently deconstructed? Or is he just a nice guy trying to do the right thing and is in fact the second coming of Christ? Similarly, with L: is he a brilliant chessmaster with a desire to stop a mass-murderer, a talent for reading human nature like an open book, and a genius that surpasses Light (considering he didn't have a Shinigami and all...)? Or is he just a paranoid neurotic who manipulates and schemes to destroy the heroic Light and ruin the utopia that he is trying to create, and is in fact the anti-christ in human form? Apparently either interpretation will get you ripped apart by ''someone'' on the right forum...
As for Light himself, it is implied that the power of the Death Note corrupts the user, and when Light returns the Death Note to Ryuk, he loses all memories of his killing and actually asks himself whether he'd be capable of killing. So is the Death Note actually responsible for Light's murders as Kira, or was he just a rotten individual all along and just drunk with power?
Some people also noticed after Ryuk took away his knowledge of the Death Note, but he regained it later, Light acted like he had multiple personality disorder. You can supposedly see it in his eyes: when his eyes are slanted he's Kira and when they're round again he's switched back to Light. Of course, near the end of the series, Kira takes over, and his eyes don't turn round again until the very last episode. Re-watch the scene in the anime when L dies. Light's eyes switch from pointed to wide while he's falling out of the chair, and he suddenly goes insane, grabs L and starts screaming. After Rem dies however, his eyes are pointed again and he's perfectly calm and collected again. Also he does tend to dissociate from his actions as Kira, even when he doesn't need to, for instance, in the manga when he explains to Ryuk: "If I blow it, Kira may have to kill his own family."
Also, in the anime, while running away, he saw a younger and more innocent version of himself. So did Light die trying to escape arrest, or was he brainwashed and snapped out of it while running away and thus, tried to find a place to hide to die alone.
Another interpretation is that he actually does care about his family. While some fans question whether he gave a damn about his father dying, some would argue he does care about them, and is actually a Yandere that wants to make the world a better place for his family like a certain other character.
He openly states that good and evil are purely subjective concepts, and whilst this doesn't necessarily disqualify someone from being Good or Evil, he never shows any inclination towards either, pursuing Kira both because it's what L would do and in order to avenge L. in the manga, it's heavily hinted (or rather speculated by Matsuda) that he kills Mikami with the Death Note in order to get final revenge for L. However, this detail is omitted from the anime, and in general the focus of his character is more on becoming L's successor than avenging him.
On that last point: while Word of God states that readers are meant to draw their conclusions about whether or not he used the Death Note on Mikami, Obata describes him as "dishonest" and "the more evil" of him and Mello.
This is complicated further by the fact that Obha has spoken more favourably of him, describing him as "blessed from above" with L's brainpower, so it really is open for interpretation.
Could it be that Near actually dislikes L since he does wear his mask in the warehouse scene, and coldly says, in response to his death, that those who can't solve the case are simply losers, or could he actually respect him judging by the fact that he admitted he couldn't beat Light alone, and tells Light, while he's acting as the second L, that while L made substantial progress on the case, Light has done almost nothing.
Misa. Could it be that she actually is just an Axe CrazyYandere or it could be argued she might have actually had some sort of trauma considering how dependent she is on that one person (Light).
Souichiro Yagami. Word of God states that he is the only character that truly fights for justice. He is quite definitely determined to catch Kira for the sake of justice, but also objects to L's more unorthodox (and less savoury and lawful) methods. However one may question just how "just" threatening an unarmed civilian at gunpoint really is. Not to mention making the trade for Shinigami Eyes and attempting to write Mello's name into the Death Note, only failing to write said name in full because Mello asks him if he's ever killed a person, leading to a moment of hesitance which proves his undoing.
Raye Penber's Stay in the Kitchen line. Is he a misogynist, or does he just want his future wife to live a normal life as a housewife so she will no longer be in the risky trade as a law enforcement officer? (For what it's worth, in the films the line is out of genuine concern for her well-being.)