type() - a better typeof

README.md

type.js - offers an more consistent type checking of native values. It relays on the [[Class]] of objects instead on typeof results.

type2.js - variation that returns "object" for wrapped natives. This one is probably more noob-immune, avoiding some possible strange situations.

Consider something like this:

// Defined by third...
var foo = new String("foo");

// ...

function noob( str ) {
    if ( type(str) !== "string" ) {
        throw new TypeError("string expected");
    }

    return ( str === "foo" );
}

If the type check returns "string", then noob will return false because of the strict equality check ===. To avoid similar situations, "object" is returned for wrapped strings, numbers and booleans.

type.js

(function($){

	var toString = Object.prototype.toString,
		classes = "Boolean Number String Function Array Date RegExp Object".split(" "),
		class2type = {};
		
	for ( var i = 0; i < classes.length; ++i ) {
		class2type[ "[object " + classes[i] + "]" ] = classes[i].toLowerCase();
	}
	
	$.type = function( obj ) {
		return obj == null ?
			"" + obj :
			class2type[ toString.call( obj ) ] || "object";
	};
	
})(this.jQuery || this);

type2.js

(function($){

	var map = {},
		toStr = map.toString,
		names = "boolean number string Function Array Date RegExp".split(" ");
		
	for ( var i = 0; i < names.length; ++i ) {
		map[ names[i].replace(/^([A-Z]\w+)/, "[object $1]") ] = names[i].toLowerCase();
	}
	
	$.type = function( obj ) {
		return obj == null && ( "" + obj )
			|| map[ typeof obj ]
			|| map[ toStr.call( obj ) ]
			|| "object";
	};
	
})(this.jQuery || this);

Hm, not sure what's your point. $.type purpose is something like typeof, but obviously it is not the same. There is many cases where typeof is not only inconsistent between browsers, but also strange in spec too ("function" only because callable). Also typeof new String("foo") === "object" is not what you wont in majority of cases.
So, yes, you can see $.type something like typeof but more useful.

What you described was not an inconsistency of typeof but more a lack of understanding of how it works.

Well, typeof implementations are not always consistent (frames, typeof alert in IE,...), and I don't think it is about a lack of understanding here, but more about understanding disadvantages of typeof and to provide an alternative when it is needed.

Those are examples of host objects which is not a failing of typeof but rather host objects exercising their freedom to be implemented how vendors wish.

Does spec saying that any callable would return "function"? Well, implementations are not consistent.
Even if typeof was perfectly consistent, it have to deal with host objects that are not consistent at all (no spec). And in that cases, its behavior is certainly not cross-browser.
We are not fixing typeof, but providing an alternative.

typeof for ES3 states

Object (native and implements [[Call]]) are "function"

typeof for ES5 states

Object (native or host and does implement [[Call]]) are "function"

There are inconsistencies even between specs (that is reasonable), I know.