Affectionate Nickname: Adam usually refers to her as "Jane." According to Word of God, this was initially because he was pretending to be a stoner and wanted to seem spacey, though he knew her real name perfectly well. Eventually it just becomes an affectionate nickname between the two. It's Serious Business when he refers to her as "Joan" in a second season episode after she disappoints him.
I Just Want to Be Normal: Zigzagged. She wants to be good at something or wishes her missions from God were something bigger like saving the world, but then gets upset when they interfere with her social life.
I See Dead People: Part of the "talking to God" package. Although according to Rocky and Judith, Joan doesn't see them every time they're around.
By-the-Book Cop: Zigzagged—he usually deferred to playing by the rules, but also realized that the various leaders of Arcadia were corrupt and often butted heads with them, insisting on following proper police procedure rather than following their demands for leniency or special favors.
Does Not Like Guns: Despite being a cop, he shows great opposition to reckless gun usage. In one episode, it's revealed that he shot and killed a robber during a bank heist, and when Luke remarks that "Dad blew a guy away—that's so cool," Will instantly shuts him down by saying that it wasn't cool; furthermore, he lives with the fact that he took another person's life every day, and has always wondered whether or not there was a better solution that shooting.
Hollywood Atheist: It's suggested that he lost his faith after Kevin's accident, as he can't believe in a God that would allow such a cruel thing to happen to his son.
To Be Lawful or Good: Many episodes dealt with Will faced with this ethical dilemma—especially because the mayor and other politicians in the city were openly corrupt and infringed on his investigations whenever possible. Will was often forced to choose between his own sense of right and wrong or the rules that Arcadia's leaders expected him to follow.
Psychic Powers: Her charism "discernment of spirits" is a form of these. It include a vision of Kevin's accidents before the cops came, psychic dreams about the synagogue fire and church vandalism, speaking to God in dreams, and seeing Judith's ghost when she visits Joan.
Mama Bear: "If someone else made those jokes about you, I would scratch their eyes out."
Big Brother Instinct: He gives a fair amount of advice to his younger siblings and offers to roll over anyone who picks on Joan.
Big Brother Instinct: Despite being the youngest, we frequently see him looking out for Joan's best interests, and Kevin gets mad at Luke for taking on the big brother role in "The Devil Made Me Do It".
The Unfavorite: His parents forget his birthday, he's frequently overshadowed by Kevin, and there's a Running Gag especially in the early episodes that no one in the family is actually listening when he talks, to the point that he's shocked when they react to something he's said.
Grace: The dude has a photographic memory. Every time he thinks he might forgive you, the image of you smashing his artwork just pops into his head. Not that I've discussed it with him.
The Stoner: Subverted. People think he's a stoner, but it's an act to keep people from getting too close and to keep Mr. Price away from his art.
Bomb Throwing Anarchist: She belongs to a group of these, most of whom dress and act exactly like her. She also occasionally spouts inflammatory rhetoric.
Brilliant, but Lazy: The second episode reveals that she's exceptionally skilled at chemistry—she just chooses not to participate in class as part of her general anti-authoritarian persona.
Bruiser with a Soft Center: Though she was genuinely tough and strong, she also had a hidden sensitive side, as indicated when it was revealed that she carries tissues with her everywhere. She also writes poetry, struggles with the cruel rumors that circulate about her, and is deeply conflicted about her alcoholic mother.
Conspiracy Theorist: She had an opinion about every subject from capitalism to hidden surveillance, and was never shy about talking about them.
Hidden Depths: Her libertarian views belie some of her more surprising traits. She's actually a skilled, intelligent student (she just doesn't buy into the idea of grades) and writes deeply moving poetry anonymously.
Strawman Political: Her extremist views are usually treated as a subject of scorn, and she's rarely portrayed as being in the right. It's most apparent in "State of Grace," when her opposition to the school's new metal detectors after a gun threat and championing of individual rights to privacy are trumped by Joan's (admittedly ambiguous) speech about the dangers guns pose and how she fears for her father's safety because of them.