Okay, here is my woeful story. I wanted my categories to be arranged by MY CHOICE, not by name, not by ID, date or anything else. My Order. It had to do with the importance of the subjects as well as the length of the words graphically.
Since list_cats() is restricted to name or ID, and the query possibilities wouldn't give me the custom list I desired, I went into the database and manually changed the ID number of every category (at the time I had 36, now I have almost 50, I think) into the order I wanted them to be in.
There, I told myself, it was done and I didn't have to worry about it any more. I had imposed my control on everything.
I then had to go in and change all the Parent/Children relationships between the categories so the "baseball cap" would show up under "hats" and not "shoes" kinda thing. But that would do it.
Now, all the posts were still associated with their category ID number which now had a different name. So posts about choosing a baseball bat were now under the category of choosing baseball shoes. Poop!
I tried going in and manually changing the database, but I have over 500 posts and every one is now in a different category. Even UPDATE SQL wasn't working for me, though I could have done it. It required a lot more concentration and stradegy than I could do at the time. I'm wiser now.
Enter the incredible and amazing ColdForged with his brilliant Enhanced View of the Post Manage Admin Screen that saved me HOURS of work. Combined with the also incredible, Batch Categories add on (not plugin - though they are working on it), which allows for batch editing, sorting, and finding of posts by category. Amazing! These two things totally saved my life with this idiot thing I did. It has been two months and I'm still finding miss-filed posts, but I think they are almost all cleaned up.
Moral of the story? Think through your categories totally before you begin, or make your changes before you add posts, or make your changes when you have less than 5 categories. Otherwise, take about a week out of your life to clean it all up if you have more than a couple hundred posts....though the plugins certainly helped tremendously.
Tread carefully. This is nothing to take lightly and backup backup backup backup!
Oh, and my site isn't about baseball, it just worked better for an analogy.