I have created Pages and placed them into the primary pull-down menu in 4.1.2, but I cannot get them to display in a proper order, I have them correctly aligned in the admin panel and they are placed in alphabetical order.  When I use the pull down menu, they have an order that will not change.

Any ideas on how to fix?

Have you published the layout?

That is what confused me the first time I tried rearranging things

Yes, I have tried to publish it as well.  Seems to just revert to the old order.  When I open up the menu in the admin CP it is now in the correct order, but still displays poorly.

I'm having the same issue with a dropdown menu on my website too. Definitely clicking 'publish', the menu item order just doesn't want to change...