Unfortunately, it looks like Google Apps Script can only retrieve the notes from a range:
https://developers.google.com/apps-script/reference/spreadsheet/range#getNotes()
There is no equivalent getComments() function.
This is an issue that has been officially raised here: https://code.google.com/p/google-apps-script-issues/issues/detail?id=1818
One of the developers has noted that:
We are aware of the demand for this feature, but there is no work going on at the moment. As a partial solution, you can use the Drive Advanced Service to read all the comments and replied on a spreadsheet, but you aren't able to create new comments or determine to which cell a given comment is attached to.
So it is possible to grab all comments, just not which cells those comments are associated with.