DMC 2 is the only entry in the series where Dante can fly freely. In DMC he hovers above the ground, where as here he can ascend and descend.
Devil May Cry 2 is the only Devil May Cry game to not feature Dantes brother Vergil. He appears in the first game as Nelo Angelo, the main antagonist of both 3 and 5, is playable in DLC for Devil May Cry 4, and is one of the main characters in the attempted "DmC" reboot
Dante's fate has never been explained. This could be due to the fact that Capcom screwed up the story so badly that the only games they can make are prequels. As of 2016 Capcom has not released a sequel to Devil May Cry 2. Every game released after Devil May Cry 2 focuses on Dante's past. This was changed in 2019 when DMC 5 was released. Not only is it set after DMC 2 but DMC 4 now takes place after 2.
The word "Ouroboros" is written on the side of Arius' helicopter. Ouroboros is the symbolization of concepts such as completion, perfection and totality, the endless round of existence, etc.
The Storyline doesn't necessarily take place immediately after the events of the first game; it could very well have happened after the events of DMC 4. This was the original plan but was changed to be set before DMC 4 with the release of DMC 5.