I am sure there's something wrong in my own code, and I am sorry I can't provide a jsbin reproducing the issue. However, when an UNCAUGHT error is thrown and the whole backtrace does not mention a single line of code outside JQuery and JqueryMobile, it is by definition a bug in either of them, even if triggered by broken code on the custom code side calling jquery.

Here the backtrace:

Uncaught TypeError: Object function (b,c,d){var e=b.split(".")[0],f;b=b.split(".")[1],f=e+"-"+b,d||(d=c,c=a.Widget),a.expr[":"][f]=function(c){return!!a.data(c,b)},a[e]=a[e]||{},a[e][b]=function(a,b){arguments.length&&this._createWidget(a,b)};var g=new c;g.options=a.extend(!0,{},g.options),a[e][b].prototype=a.extend(!0,g,{namespace:e,widgetName:b,widgetEventPrefix:a[e][b].prototype.widgetEventPrefix||b,widgetBaseClass:f},d),a.widget.bridge(b,a[e][b])} has no method 'extend' jquery.mobile-1.3.1.js:586
$.Widget._createWidget jquery.mobile-1.3.1.js:586
$.(anonymous function).(anonymous function) jquery.mobile-1.3.1.js:416
(anonymous function) jquery.mobile-1.3.1.js:559
jQuery.extend.each jquery.js:660
jQuery.fn.jQuery.each jquery.js:271
$.fn.(anonymous function) jquery.mobile-1.3.1.js:554
(anonymous function) jquery.mobile-1.3.1.js:1116
jQuery.event.dispatch jquery.js:3332
elemData.handle.eventHandle jquery.js:2941
jQuery.event.trigger jquery.js:3210
(anonymous function) jquery.js:3869
jQuery.extend.each jquery.js:660
jQuery.fn.jQuery.each jquery.js:271
jQuery.fn.extend.trigger jquery.js:3868
$.extend.initializePage jquery.mobile-1.3.1.js:11102
(anonymous function) jquery.mobile-1.3.1.js:11168
fire jquery.js:1075
self.fireWith jquery.js:1193
jQuery.extend.ready jquery.js:435
DOMContentLoaded jquery.js:949

One of the reasons I can't provide a test case is the nature of the issue itself: it's not giving me any clue about what code of mine is triggering the issue, and I can't reproduce my whole website on a jsbin.

If I am doing something wrong in my code (which is _certainly_ the case), then either jquery or jquerymobile _must_ throw an understandable error message explaining how it is being abused, unless it can be evinced from the backtrace.