function getElementsByTagName(node, nodeName){
    for(var
        tmp = document.createElement("tmp"),
        childNodes = tmp.appendChild(node) && tmp.getElementsByTagName(nodeName),
        i = 0, length = childNodes.length,
        result = [];
        i < length; ++i
    )
        result[i] = childNodes[i]
    ;
    childNodes = tmp.childNodes;
    length = childNodes.length;
    while(length--)
        node.appendChild(childNodes[0])
    ;
    return tmp = result;
};

could be probably smaller via while ...

    while(childNodes = tmp.firstChild)
        node.appendChild(childNodes)
    ;

not sure which one will perform better though ... I'll try some bench later

so … what about this? Still talking about performances, I do like your solution.

function getElementsByTagName(node, nodeName){
    for(var
        tmp = document.createElement("tmp"),
        childNodes = tmp.appendChild(node) && tmp.getElementsByTagName(nodeName),
        i = 0, length = childNodes.length,
        result = [];
        i < length; ++i
    )
        result[i] = childNodes[i]
    ;
    childNodes = tmp.childNodes;
    length = childNodes.length;
    while(length)
        node.appendChild(childNodes[--length])
    ;
    return tmp = result;
};

The node list doesn’t need to be live. This is an internal method just for use by selector engines.

Your solution is a good idea but unfortunately it does not work because of a behaviour unique to document fragments. Once you append a document fragment to an element, the fragment disappears and the fragment’s children become direct children of the element that the fragment is appended to. I hope I explained that properly.

function getElementsByTagName(node, nodeName){
    var tmp = document.createElement("tmp");
    return tmp.appendChild(node) && tmp.getElementsByTagName(nodeName);
};

elements.item = function (i) { return this[i]; };

function getElementsByTagName( node, tagName ){

};