Bearing in mind it's age, of course, it is horribly dated. The camera angles are sloppy and leave your enemies out of the frame quite often which, for me, is a no no.
Capcom seem to have this love of making you fight the same bosses/enemies more than once (they do this with resident evil too) and the whole part where Dante has to re-fight everyone again? Lazy, lazy, lazy.
The scripting is dreadful, Dante's one-liners wouldn't be out of date in an early 90's high school TV sitcom and there are parts where you have to essentially button mash-sorry, do "combos"-in order to get to bit you want (those statues with rings of candles/flames on them that you need to get a certain rank on). If you can't mash, you're stuck.
And I don't like Lady's hair.