jQuery dropdown plugin
From a once over:


Your code is not consistently indented, especially the first dozen lines need some TLC
$.component = function( name, object ) { needs commenting, it is not clear what this is trying to achieve.
evt is an unfortunate parameter name, I would go for the classic e or the readable event
$targ is needlessly short, just use $target
You could probably use helper functions for if(evt) evt.preventDefault(); and if(evt) evt.preventDefault(); evt.stopPropagation();
Note that if(evt) evt.preventDefault(); evt.stopPropagation(); is exactly the kind of bug that makes people enforce {} around if blocks!
toggle() could use a ternary condition with !this.isShowing
'show-mobile-nav' should probably not be hardcoded since you use it more than once, instead you should use a properly named variable


All in all, some pretty cool code.