These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Also "FACE", the opening theme. Hey! Boy! Looking for your soul! The second ending theme, "Hikari" by Kyoko's voice actress Saeko Chiba is pretty nice, too.
Cry for the Devil: The show invokes this trope with most of its bad guys (except Noriega). Clair is probably the most prominent example, which plays out over the course of the entire series; but you see it with Shun too.
Designated Villain: Toward the end, some characters view Clair as a villain when he obviously isn't in that villainous a position anymore.
In a somewhat unusual case, though, the show seems to deliberately encourage it—particularly in Clair's case, as the flashbacks to him and his abusive father start good and early, and he gets more and more heroic/sympathetic things to do as the series goes on.
Foe Yay: Most of the fanfiction in this teeny tiny fandom is DaisukexClair, even though they normally do not get along. Except towards the end, where they help each other, but not actually for yaoi reasons.
There's also a little of this between Kyoko and Mitchal, when Kyoko comes to rescue Daisuke, and there are those who ship them.
Fridge Brilliance: Shun effortlessly beats up Daisuke earlier in the series, but in the finale Daisuke has the upper hand. Is it heroic resolve? No, it's that Shun still hasn't completely recovered from the sniper bullet that went through his chest not too long ago
Fridge Logic: If Monica can barely manage to earn enough to pay for the trailer she shares with her mother, how can she afford to keep a donkey? And how is said donkey housetrained if there's no way it can fit into their trailer home?!
Moe: In a way, Clair. He comes off this way owing to his presentation as a childish Ill Boy and his really crappy childhood. It helps that he's also really, really cute.
The Scrappy: Again, Lorenzo. Many fans hate him for the way he treated Clair. Rumie as well, in this case much less justified.
Squick: Shows up every so often, to the point it suggests that the characters just don't have very high standards for cleanliness or hygiene. Examples include:
There's a city in Judoh's Absurdly Spacious Sewer. Furthermore, the children who live down there apparently think nothing of playing in the sewer water, nor does Daisuke think anything of jumping in to retrieve his bullet necklace.
Clair's initiation ritual for becoming Vampire involves him cutting his finger and dripping blood into a big vat of wine, from which everyone in attendance drinks.
After Noriega kills Ian, he sends (it's implied) Ian's hand back to Clair, Giovanni, and Mitchal in a box. This is already squicky enough, but then Clair fishes the ring he was wearing out of the box with a horrible squelching noise and sticks it on his own finger—without cleaning it first!
Superlative Dubbing: The English dub of this series is widely considered to be virtually flawless and every bit as enjoyable as the Japanese.