Highlight new Reddit comments with this GreaseMonkey user script.

Reddit_Highlight_New_Comments.user.js

// ==UserScript==
// @name			Reddit: Highlight New Comments v3
// @description	Highlights comments on Reddit that are new since your last visit.
// @author		Chris H (Zren / Shade), Nathan Sweet
// @icon			https://reddit.com/favicon.ico
// @namespace	http://xshade.ca
// @version		1
// @include		/https?:\/\/((www|pay|[a-z]{2})\.)?reddit\.com\/r\/[a-zA-Z0-9]+\/comments\/.*/
// @grant		GM_addStyle
// ==/UserScript==

// This is a GreaseMonkey user script that highlights comments on Reddit that are new since your last visit.
// Based on: https://openuserjs.org/scripts/Zren/Reddit_Highlight_New_Comments/source

(function () {
	// You can remove .res-commentBoxes if you're not using RES.
	var style = " \
.new-comment .usertext-body { \
background-color: transparent; \
border: 0; \
margin: 0; \
} \
\
.res-commentBoxes .comment.new-comment, \
.res-commentBoxes .comment .comment .comment.new-comment, \
.res-commentBoxes .comment .comment .comment .comment .comment.new-comment, \
.res-commentBoxes .comment .comment .comment .comment .comment .comment .comment.new-comment, \
.res-commentBoxes .comment .comment .comment .comment .comment .comment .comment .comment .comment.new-comment \
{ background-color: #f2f8ff !important; border: solid 1px #d6e3f3 !important; } \
\
.res-commentBoxes .comment .comment.new-comment, \
.res-commentBoxes .comment .comment .comment .comment.new-comment, \
.res-commentBoxes .comment .comment .comment .comment .comment .comment.new-comment, \
.res-commentBoxes .comment .comment .comment .comment .comment .comment .comment .comment.new-comment, \
.res-commentBoxes .comment .comment .comment .comment .comment .comment .comment .comment .comment .comment.new-comment \
{ background-color: #e5efff !important; border: solid 1px #cddaf3 !important; } \
";

	// Overwrite Reddit's default styling.
	GM_addStyle(style);

	function embed () {
		// --- Settings
		var threadTTL = 3 * 24 * 60 * 60 * 1000; // 3 Days

		// --- Variables
		var nowAtLoad = Date.now();
		var lastVisitedAtLoad = null;

		// --- Functions
		var getThreadId = function () {
			var element = document.querySelector('[rel="shorturl"]');
			return !element ? null : "redd_id_" + element.href.substr(-6);
		};

		var setThreadLastVisited = function (id, t) {
			localStorage.setItem(id, (typeof t === 'object' && t.getTime) ? t.getTime() : t);
		};

		var getThreadLastVisited = function (id) {
			return parseInt(localStorage.getItem(id), 10);
		};

		var deleteThreadLastVisited = function (id) {
			localStorage.removeItem(id);
		};

		var highlightNewCommentsSince = function (t) {
			$('.comment').each(function (i, comment) {
				comment = $(comment);
				if (comment.hasClass('deleted')) return;
				if (new Date(comment.find('.entry > .tagline > time').attr('datetime')) > t)
					comment.addClass('new-comment');
				else
					comment.removeClass('new-comment');
			});
		};

		var updateLastVisited = function () {
			var id = getThreadId();
			var threadLastVisited = getThreadLastVisited(id);
			if (threadLastVisited)
				highlightNewCommentsSince(threadLastVisited);
			else
				threadLastVisited = nowAtLoad;
			setThreadLastVisited(id, nowAtLoad);
			lastVisitedAtLoad = threadLastVisited;
		};

		var purgeExpiredData = function () {
			var idRegex = /redd_id_([a-zA-Z0-9]{6})/;
			Object.keys(localStorage).forEach(function (id) {
				if (!idRegex.test(id)) return false;
				if (nowAtLoad - threadTTL >= getThreadLastVisited(id)) deleteThreadLastVisited(id);
			});
		};
		
		var update = function () {
			if (lastVisitedAtLoad)
				highlightNewCommentsSince(lastVisitedAtLoad);
			else
				updateLastVisited();
			purgeExpiredData();
		};
		
		// --- Main
		if (!getThreadId()) return;

		// Wrap the function called when requesting more comments.
		var morechildren_reddit = morechildren.__original__ || morechildren;
		morechildren = function () {
			morechildren_reddit.apply(this, arguments);
			setTimeout(update, 1000);
		};
		morechildren.__original__ = morechildren_reddit;

		update();
	}

	var inject = document.createElement("script");
	inject.setAttribute("type", "text/javascript");
	inject.appendChild(document.createTextNode("(" + embed + ")()"));
	document.body.appendChild(inject);

})();

If the thread you are looking at has an underscore in the name, you will need to change the @include to /https?://((www|pay|[a-z]{2}).)?reddit.com/r/[a-zA-Z0-9_]+/comments/.*/