VisioOnline: Comment Object example. https://dev.office.com/reference/add-ins/visio/comment.

comment.js

 Visio.run(function (ctx) { 
    var activePage = ctx.document.getActivePage();
    var shapeName = "Position Belt.41";
    var shape = activePage.shapes.getItem(shapeName);
    var shapecomments= shape.comments;
        shapecomments.load();
        return ctx.sync().then(function () {
          for(var i=0; i<shapecomments.items.length;i++)
        {
                 var comment= shapecomments.items[i];
         console.log("comment Author: " + comment.author);
         console.log("Comment Text: " + comment.text);
           console.log("Date " + comment.date);
        }
     });
}).catch(function(error) {
        console.log("Error: " + error);
        if (error instanceof OfficeExtension.Error) {
            console.log("Debug info: " + JSON.stringify(error.debugInfo));
        }
});