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_{^{Not to be intentionally pedantic, but we are here to discuss things like coding conventions.}}

I find myself disliking how you switch from one style to another within the same method.

 if (o === n) {
 return 'null';
 }
 /*********
 * If we made it this far, just return the set the
 * r variable and return at the end;
 *********/
 switch (o) {
 case g:
 r = 'global';
 break;
 case g.document:
 r = 'htmldocument';
 break;
 default:
 break;
 }

This switch statement could be written (shorter) as two if statements (and the comments add nothing to the function).

The r variable is unnecessary (anywhere it is used can be replaced with a return statement).

The rest of the variables within that function are constants WRT it.

I would rewrite this whole thing like so:

/*jslint maxerr: 50, indent: 4 */
(function (g, Object, n, u) {
 "use strict";
 var nodeType = {
 1: 'element_node',
 2: 'attribute_node',
 3: 'text_node',
 4: 'cdata_section_node',
 5: 'entity_reference_node',
 6: 'entity_node',
 7: 'processing_instrction_node',
 8: 'comment_node',
 9: 'document_node',
 10: 'document_type_node',
 11: 'document_fragment_node1',
 12: 'notation_node'
 };
 Object.typeOf = function (o) {
 if (o === u) {
 return 'undefined';
 }
 if (o === n) {
 return 'null';
 }
 if (o === g) {
 return 'global';
 }
 if (o === g.document) {
 return 'htmldocument';
 }
 if (o.nodeType && nodeType[o.nodeType]) {
 return nodeType[o.nodeType];
 }
 return ({}).toString.call(o).match(/\s([a-z|A-Z]+)/)[1].toLowerCase();
 };
}(this, Object, null));