No way to check if an entry in the JSON actually exists.

[abledbody]

Say you have a JSON that looks like this:
{ "someThing": { "fieldA": 10.0, "fieldC": 5.0 } }
And some code that looks like this:
var fieldB = json["someThing"]["fieldB"]
There's no way to check if you successfully found an entry in that spot. If you try and access the value, float fieldBValue = fieldB it will simply fail an assertion.
I recommend changing most of the assertions in Json class to exceptions, so that they can be caught and handled by the user of the API.

[abledbody]

Also, adding a new entry in the internal dictionary every time you can't find a key is an extremely bad idea, because it allocates more memory for an action that shouldn't even (noticeably) mutate the class. This should also be an exception.