samples are better than long explainations so:
var oParent = new Element("div", { backgroundColor: 'green' }), oTD;
oParent.update("<table><tr><td id='myTD'></td></tr></table>");
oTD = oParent.getElementsBySelector('[id=myTD]')[0]; // works fine
// -> oTD element
oTD = oParent.getElementsBySelector('TD')[0]; // works fine
// -> oTD element
oTD = oParent.getElementsBySelector('#myTD')[0]; // bugs on IE but ok on firefox
// -> oTD 'undefined'
$(document.body).appendChild(oParent); // let's append the elements to the doc
oTD = oParent.getElementsBySelector('#myTD')[0]; // now works
// -> oTD element