There are so many things that are poorly thought out or underspecified in JSON, it's amazing that it got so widely adopted for interop. No wonder that it became a perpetual source of serialization bugs.
Especially annoying given that they could have been easily adopted. Infinity could've been encoded as `1/0` (among most other possibilities). NaN could've been encoded as `0/0` (again, among most other possibilities). JSON doesn't allow all possible JavaScript literals anyway, so these encodings might have been worked if they were somehow standardized.