The FSF says of the JSON License:
This ["not-for-evil" term] is a restriction on usage and thus conflicts with freedom 0. The restriction might be unenforcible, but we cannot presume that. Thus, the license is nonfree.
Similarly it is not open source because it conflicts with term 6 of the Open Source Definition, "No Discrimination Against Fields of Endeavor".
The use of this license by some FLOSS project is as roughly as problematic as any other non-FLOSS license. It introduces a non-free term in how the software may be used, just like a license that restricts, e.g., commercial use of the software.
If the project is otherwise permissively-licensed, this doesn't cause a legal problem, but only a practical one about how the resulting software may be used (i.e., only for "good", rather than for all purposes).
If the project uses a copyleft license like the GNU GPL, this does introduce a legal problem. The GPL applies to the work as a whole, and the GPL forbids the introduction of restrictions beyond what the GPL itself requires. If a project maintainer accidentally included code under the JSON License within the distribution of a GPL-licensed work, copyright holders of the GPL-licensed parts could take legal action for violation of their software's GPL terms.
As the FSF notes, it's possible that this not-for-evil term might be altogether legally void. If that possibility proves true in any particular jurisdiction, then the JSON License would, in effect, be a FLOSS license in that jurisdiction.