I'm sure most of us have seen or heard some filters continue to ring after receiving a short duration of a tone burst. Some may not think it's a problem, but it can be.
One example is the famous third octave filter. Almost everyone I know that has used on of those things to flatten a PA system says it doesn't sound right when they use it but don't know why. Well it's frequency response is much flatter but why doesn't it sound right?
It's simple really, think of it like you are playing a series of stacatto notes a semitone apart. Nothing wrong with that but if the filters continue ringing then you effectively have two of those notes being played at the same time which is not what you wanted and can sound really bad.
Then look at complex music and consider what happens when the filters are constantly ringing. Hey wait a minute, that's not right. It's like having reverb that shouldn't be there.
That's all it is.