How to find all of the responses to a published research paper?
First, it may depend on your field, but at least in mine (physics and chemistry), it is rare for papers to generate comments or replies, and really extraordinary for a paper to be followed by multiple comments. (The editor usually lets the original authors reply to the comment, however.)

Some publishers provide links to the comments and replies on the webpage for the original paper. Otherwise, you can locate those comments using the following criteria:


they are published in the same journal, or in a preprint server (like arxiv)
their title includes “comment on” or “reply to” (or other such publisher-dependent prefix that you need to identify)


Finally, you should get the list of all newer papers citing the original paper, and check them out. If you're investigating a paper in depth, you’ll do that anyway :)