The Google AMP test has a secondary section used to validate the structured data specified for AMP pages. Although this is an optional aspect, it's a best practice to have even the structured data section fully validated as in the image below:
In the case that you get errors for the structured data section, ensure that all mandatory meta tags have been specified under the configuration of JAmp -> tab 'Metadata'. It's important that you fill in all required values as in the image below, for more informations refer to the PDF docs at the paragraph 'Metadata':
In the case that you still get errors when opening the details page of the structured data report by clicking on 'EXPLORE OPTIONAL VALUES', pay attention to the data type for which errors are reported.
Indeed AMP and JAMP only deal with the 'NewsArticle' structured data. Commonly there could be extensions that specify generic structured data in a page not thought for Google AMP and that could be seen and reported as wrong during the AMP test.
If this is the case, you can just ignore those errors because not relevant for the Google AMP format, the only type of the structured data that must be validated is the 'NewsArticle' one. Other generic types to ignore could be 'Article', 'Blog', 'Product', 'Review', 'Breadcrumb', etc
Why the AMP test reports invalid structured data?