Quoted keys, strict comma rules, very limited data types, are the main ones. There are a host of others if you view it through the lenses of user-read/write, and a different set of issues if you view it as a machine data interface. Trying to combine the two seems fundamentally misguided.
Lack of comments seems like a big one seeing as it's so widely used for "configuration". It's a big enough downside that VSCode and others have violated it via ad-hoc extensions of the format.
The comma rules introduce diff noise on unrelated lines.
Personally the only thing I miss from it is support for binary data - you end up having to base64 binary content which is a little messy.