You can expect to install anything from the repositories without a serious problem. With multiple DE you sometimes have what are considered cosmetic issues, all of which you can configure.
Of course, some people find these "cosmetic" issues more or less annoying, but, they will not prevent the applications or system from working.
Each DE tends to have a set of applications for editing, multi media, etc so you will end up with duplicate applications.
All of the basic applications will work on any DE or WM. The only real conflict is that you can run only one WM at a time (so you can not run kwin at the same time as unity).
In the event you have a problem, ask a more specific question.