What is the main problem with using HTTP methods in this case - Incorrect use of HTTP methods violates RESTful architecture and API readability - Errors are returned not in JSON format - Non-standard headers in GET requests - GET requests are not cached - Conflicts due to incorrect semantics of methods - Routing violates RESTful principles

The main problem with the incorrect use of HTTP methods in RESTful APIs is the violation of HTTP method semantics, which leads to confusion and reduces the readability and predictability of the API. For example, using GET for data modification operations contradicts standards and can cause issues with caching, security, and routing.

Other listed problems (JSON errors, non-standard headers, GET non-cacheability, conflicts due to semantics, routing violations) are often consequences of improper application of HTTP methods and REST architectural principles. Therefore, the key is to adhere to the correct semantics of HTTP methods (GET for reading, POST for creating, PUT/PATCH for updating, DELETE for deleting) to ensure the API functions correctly and is understandable for clients.