Is parsing JSON on the serverside dangerous?
JSON data can only contain basic types: strings, numbers, Booleans, null, objects, and lists.  This means that properly formatted JSON data poses no risk at all to your application, unless you are doing something silly like executing that code with eval().
So if valid JSON is not an issue, the question becomes "can a client send any invalid data that poses a security risk when processed by Python's json module".  The answer here is also no, Python's json module will reliably raise a ValueError for invalid json data, with no scary side effects.
I'm writing a Python application with Django and serializing objects to and from JSON using Python's standard json library.
I've heard something along the lines that 

any seralizer/deserializer/parser is a potential security threat to the application

Is this really true on the serverside? Do I need to fear someone sending tampered JSON up to my instance and them having remote code execution privileges? I would think that there wouldn't be any security threats other than (potentially) XSS or SQL injection, which in my case (converting values to ints, storing all data in MongoDB) shouldn't be the case.
Should I be paranoid along these lines of parsing JSON data from clients?