One issue is that it's surprisingly poorly specified: http://seriot.ch/parsing_json.php.

As a data-interchange format, it lacks first class dates/timestamps, the issues about specification are a pain when dealing with numbers (depending on language, you may not be able to use the full range of 64 bit ints), and has no builtin concept of schemas. That said, I'm not sure what I'd recommend above JSON, though you clearly wouldn't use it for really high performance servers.

It's also used as a configuration language, where more issues surface. It doesn't accept trailing commas or comments (I can see the argument for requiring all keys to be quoted, but that's a pain to write as well). For configuration, I think I prefer TOML to JSON. Dhall looks cool, but I've never used it.