-CORS support. Deploy this to a non-local domain and try to reach it from a web browser and it will fail. I like https://github.com/rs/cors. I had rolled my own but then moved to that library.
- input validation. I like go-playground/validator.
The other big issue is the locking by hand around the task store. In reality usually there would be a database to handle concurrent read/writes. I use SQLite in production. I know this is just a demo and you want to use just stdlib, but serializing all data access is sort of unacceptable as a solution in a concurrent language like Go. When I'm not handling concurrency with SQLite I like to implement The actor pattern, having a persistent goroutine listen and respond to "taskstore" requests via channels.