Not sure how this will help with DMC4 but here goes:
(Pretty much all of these appear in DMC1 and 3, a couple might not have in DMC2, but I still count them as 'tradition'. The gameplay aspects focus more on Dante as Nero is a new character with new concepts)
Moves:
Attacks - Stinger, High Time, Helm Breaker
Movement - Air Hike, Kick Jump (off of wall), Roll
Other - Devil Trigger, some ability that lets you freeze time temporarily (1 had Time Bangle, 2 had an amulet granting you the power with DT attacks, and 3 had the Quicksilver style)
Weapons: Rebellion, Gauntlets, Ebony and Ivory, Shotgun, 'Heavy' weapon (i.e. Grenade/Rocket/Missile launcher)
Missions:
Not sure what I can say really. Most of them have had around 20 missions, with plenty of bosses. Most of them have at least one recurring boss - DMC1 had many, DMC2 had Bolverk and DMC3 had Vergil (and all of them if you include M18 where you can fight them all again).
Difficulty Modes:
Well usually there's Easy (which is usually 'dumbed down' a bit, and not really a good challenge like DMC should be), then there's Normal, which is generally a challenge for new players but doable, then Hard, and Dante Must Die! Which is for the people who really like a challenge. DMC4 has changed the names of the modes (to Human, Devil Hunter and such), but they should basically be the same. The hardest will probably still be named Dante Must Die! (or Nero Must Die!). Usually, there is unlockable content for beating each mode, namely costumes, some which grant extra power (i.e. infinite DT).
Storyline:
Legend of Sparda (bound to be mentioned), Yamato, some kind of family history.
Possibly 'Jackpot' scene (where Dante's guns get powered up and shoot a finishing blow)
Female lead character - DMC1 had Trish, DMC2 had Lucia, DMC3 had Lady and DMC4 has Kyrie.
Misc:
Costumes - DMC1 costume, Legendary Dark Knight, Super Dante
This is all I can think of right now.. I'm sure theres more though.