it appears that earlier IEs don't like the <section> tag much, either
here is a way of making your script cross-browser (provided you don't have a problem with textNodes, too

)
Code:
<!DOCTYPE html>
<html dir="ltr" lang="en">
<head>
<meta charset="utf-8"/>
<title>Table of random alpha characters</title>
<style>
#result
{
margin: 10px;
}
#randomTable
{
border: 1px solid #000000; /* Black. */
border-collapse: collapse;
}
#randomTable td
{
border: 1px solid #000000; /* Black. */
text-align: center;
height: 50px;
width: 50px;
}
</style>
</head>
<body>
<article>
<section id="buttons">
<input type="button" id="generateButton" value="Generate"/>
</section>
<div id="result"></div>
</article>
<script>
/*jslint browser: true, vars: true, white: true, maxerr: 50, indent: 4 */
(function ()
{
"use strict";
function removeChildren(parent)
{
while (parent.hasChildNodes())
{
parent.removeChild(parent.firstChild);
}
}
function createTable(id, rows, columns, generator)
{
var alph = "abcdefghijklmnopqrstuvwxy".split("");
var table = document.createElement("table");
table.setAttribute("id", id);
alph.sort(generator)
var body = document.createElement("tbody");
var b=0
var r = null;
var c = null;
for (r = 0; r < rows; r += 1)
{
var row = document.createElement("tr");
for (c = 0; c < columns; c += 1)
{
var cell = document.createElement("td");
if(cell.hasChildNodes()){
cell.removeChild(cell.firstChild)
}
var txt = document.createTextNode(alph[b++])
cell.appendChild(txt);
row.appendChild(cell);
}
body.appendChild(row);
}
table.appendChild(body);
return table;
}
function fetchRandomAlphaCharacter()
{
return (Math.round(Math.random())-0.5);
}
function initialize()
{
var resultSection = document.getElementById("result");
var generateButton = document.getElementById("generateButton");
generateButton.onclick= function (){
removeChildren(resultSection);
resultSection.appendChild(createTable("randomTable", 5, 5, fetchRandomAlphaCharacter));
}
}
window.onload=initialize;
}());
</script>
</body>
</html>
you may note that I reverted to the previous random letter generator as mrhoo's otherwise excellent suggestion creates multiple instances of the same letter, which I don't think OP was talking about...