The API uses the REST architecture. So it is basically making GET, POST, PUT, and DELETE requests via HTTP to identify a resource and/or perform an action on the resource, which, of course resides in the database.
What exactly are the concerns for using it in production?
I'd say the biggest con is that the API is fairly limited and Solarwinds support for it is equally limited.
The API will do exactly what is says, but like Justin said it is very limited. Make sure it does everything you want it to before you venture down this road. It is limited in surprising ways. And it appears Solarwinds has no interest in making it a worthwhile API. They don't even use it in house.