REST API testing common issues

I have recently started testing rest based web services. I am wondering what are common issues faced while testing them.

I generally look for

1. response status (http code is among 200/400/500)

2. response headers (cache control, response type, content length )

3. if expected fields / values are present in json response.

I want to know what else to look for and issues in general while testing rest based web services