You got some valid and some not so valid points here
> * It reloads the page 3 times, actually stepping through an edit form,
> modifying wikitext with JS, and saving.
Three times? More like two.
> * It is 1100 lines of ugly code.
1049 but 'ugly' is a bit over the top.
> * It isn't localised.
> * It breaks if translations or aliases of the Category namespace are
> used.
That is one point (the aliases). Localisation is otherwise irrelevant,
as there is nothing to localize.
> * It adds random text to the category display, instead of using nice
> icons.
Why would you call the + - and +/- links "random text"? And why would
icons be "nice"?!
> * It doesn't prompt for an edit summary, nor does it provide any sort
> of confirmation.
Confirmation should be evedent, as the page reloads with the category
list changed. An edit summary is provided automatically
> By contrast, my newer version:
> * Submits an edit through the API, and selectively reloads the
> category section with no user disruption other than a progress spinner.
That is indeed nice.
> * Is 300 lines of simple jQuery code.
Also nice. I hope jQuery becomes standard very soon. It was not easily
available when hotcat was developed
> * Is fully localisable.
Thats nice too, but see above
> * Has full support for translations and aliases of the category
> namespace.
Good
> * Uses icons for the actions.
Not necessarily an improvement
> * Prompts for confirmation and an edit summary before making an edit.
Hm, that is somewhat of an inconvenience if you have to change
multiple categories, or does your version gather changes and submit
them in one edit and one summary?