getContext is not a function

Your value:

this.element = $(id);

is a jQuery object, not a pure Canvas element.

To turn it back so you can call getContext(), call this.element.get(0), or better yet store the real element and not the jQuery object:

function canvasLayer(location, id) {

    this.width = $(window).width();
    this.height = $(window).height();
    this.element = document.createElement('canvas');

    $(this.element)
       .attr('id', id)
       .text('unsupported browser')
       .attr('width', this.width)       // for pixels
       .attr('height', this.height)
       .width(this.width)               // for CSS scaling
       .height(this.height)
       .appendTo(location);

    this.context = this.element.getContext("2d");
}

See running code at http://jsfiddle.net/alnitak/zbaMh/, ideally using the Chrome Javascript Console so you can see the resulting object in the debug output.