One of the things that I've often encountered is a granularity/association problem: tasks often become either Omnibus tasks where there's a shitload of stuff jammed into a single task, or a spread out mishmash of related tasks that don't have very good linking between them.
A good example would be a web development feature. I'm going to do the backend, someone else is going to do the frontend. Those are two pretty distinct tasks, but there's a lot of shared communication there. And most PM systems I've used don't have a (good) way to link those together. Mostly in my experience, 3rd party tools end up getting used, with links to shared wiki/moqups/google docs/dropbox whatever.
If I need to have 7 tabs open (email, slack, trello, moqups, google docs...) to get all the information I need to figure out what I need to work on next, my PM system isn't serving me very well.