Detect paragraph element change with JQuery

You can use 'DOMSubtreeModified' to check the dom changes on html tag elements. See the support for this event across browsers.

http://jsfiddle.net/nnbqye55/7/

$(document).on("DOMSubtreeModified", "#test", function () {
    alert("Paragraph changed");
});

change events won't fire on the paragraph. What you need are known as Mutation Observers. Here is the relevant MDN documentation. They have pretty good browser penetration; for older IEs, you can probably use the deprecated Mutation Events, though those are known to be performance killers, so be very careful. I'll rewrite your example using Mutation Observers; you can also check out a jsFiddle demo:

$(function(){
    //Store the test paragraph node
    var test = $('#test');

    //Function to change the paragraph
    var changeParagraph = function () {
        var d = new Date();
        var time = d.getHours() + ":" + d.getMinutes() + ":" + d.getSeconds();
        test.text(time);
    };

    //Bind the paragraph changing event
    $('#submit1').on('click', changeParagraph);

    //Observe the paragraph
    this.observer = new MutationObserver( function(mutations) {
        alert('Paragraph changed!')
    }.bind(this));
    this.observer.observe(test.get(0), {characterData: true, childList: true});
});