As requested by Ryaniel here's what I think were the good points of Devil May Cry 2:
1) Dante's design. Outfit and face/etc. He still looks as cool as in every other Devil May Cry.
2) That move where you can avoid EVERYTHING by just pressing O is incredible. I love it.
3) Also O introduced some trickster moves as well, where Dante could walk on buildings etc etc.
4) Rebellion. It was a great idea to invent a sword just for Dante alone and not some relic of Sparda. (Like Force Edge which was Sparda's primary weapon I mean).
5) Devil Trigger. It has to be the most awesome Devil Trigger in the 3 first games concerning appearance. Who knows why they created "that thing" for Dante's Devil Trigger in Devil May Cry 3. Also while on Devil Trigger you many new moves.
6) Desperation Devil Trigger. It was a good idea. While at it not only you get more powerful but you get new moves as well(moves that even normal Devil Trigger has not).
7) Lucia's DIESEL clothes. I have to say that although she sucked at her usual outfit, she was kinda hot in the casual clothes.
8) The environment. I love (almost) every place. It has a village, a city, a demon realm, ruins and some other places which are not only designed to look nice, but you have plenty of space to move as well. Even in the elevator you were free as hell. I loved that.
9) Introduction of Bloody Palace. We love it in Devil May Cry 3. But in Devil May Cry 2 it allows you to fight enemies only found in secret mission. It's pretty neat.
10) Dante % Motorcycle. It has to be one of the coolest cut-scenes of the game. Too bad there wasn't a mission where he runs with, but I guess it's natural.
11) Aerial moves. Back there in Devil May Cry, you only had Killer Bee and Helm Breaker. Now Dante can perform kicks, sword attacks and few other moves which keep you and the enemy on air.
12) Dante's Grenade Launcher. It has to be Dante's greatest Grenade/Gun/Launcher in the first 3 games. Not only it goes fast/far and it is powerful, but it allows you to shoot in the air and stay airborne as well, since Dante shoots with Ebony if you have the Grenade Launcher equipped and try to shoot while jumping.
13) Graphics. Not throughout the game but in cut-scenes. In the cut-scene where you fight the building monster the graphics might even look better than Devil May Cry 3's cut-scenes. I love them there.
14) The Despair Embodied. It was WAY cooler than half dead Mundus and in the last mission of Devil May Cry.
15) Trish as a secret character. Not only powerful but awesome as well. Wielding Sparda and Luce & Ombra was nice.
16) DMC1 Dante. This time you not only get the appearance but Devil May Cry 1 soundtrack as well. Brilliant idea.
17) Lucia's character concerning gameplay. A character that only uses swords and daggers was nice, and on top of it being woman as well. The bad thing is that they picked Lucia, but the idea rocked if you ask me.
18) Dante in the last mission has to be the coolest and less cheesy Dante in last missions so far. Remember. Devil May Cry: The infamous LIIIIIGHT scene. Devil May Cry 3: my soul IT SAYS IT WANTS TO STOP YOU!!!!. Ok in there even Vergil laughs
. Devil May Cry 2: Nothing cheesy just. D: I'm going. L: Don't you want to hear the story about Sparda from Matier? D: I know..he did the same thing. Awesome^^
19) Also the game's idea is that Dante offers his services in places throughout the Earth in general. Protecting anyone who would ask him help against demons. The pictures, videos etc. Show him in high places observing and going immediately down if he spots something bad. I like that idea about Dante. It was just portrayed wrong/bad.
20) Soundtrack. I like it a lot. It is not gothic like music like Devil May Cry has nor it is metal fast paced music like the one in Devil May Cry 3. (I love them all by the way). But I think that it fits the game perfectly.
..and few other things.
Now about Sparda. Well is it mentioned (in Devil May Cry 1) that he was helped by humans in his quest to kill demons? All I remember in the prologue is: But someone from the Underworld woke up to justice and stood up against this legion, alone. His name was Sparda. Later, he quietly reigned the human world and continued to preserve harmony...Until his death. He became a legend. The Legendary Dark Knight Sparda"
Unless you mean some other place in Devil May Cry 1 where Sparda's name is involved? Please fill me in about it, I'm curious.