Something miraculous happened. I found out that I could move around widgets and save arrangement again. I haven't done anything myself consciously. Although when I was aware of the problem I did address my issue to blogger using the complain button (within blogger options on layout upper right corner, the gear thingy). I figured they must have applied some of their magic without me knowing. Or it could be that without realizing I might have removed a script or widget that apparently was causing the issue. If I had to guess it could be a third party related posts widget I had used on many individual posts. It was not working properly anymore and forced me to remove the script from all the posts I had placed it in. (Very tedious and a lot of work I can tell you.) Could also be that the new linkwithin widget I installed (just now) fixed the issue for me. So maybe there is some truth to certain widgets corrupting the arrangement. This means it could be wise to remove all the widgets and then install them again to see which one is causing the issue. Just sayin!
After adding a new html widget in my blogger layout I discovered I could not save my arrangement. Meaning that I could not move it around and switch with another widget. I was able to do so before this just fine. Now many possible solutions have been given (when you google it) and none of them seemed to do the trick for me. However there was one tip that did work. Although it requires you to copy and paste the widgets manually in EDIT HTML. I know that might scare off some people. But underneath there is a screencast made by Prayag Verma (a Blogger Template Specialist) that shows you how. Here is where you can find him:
It's actually very simple to do. (But always make a backup of your template before editing HTML so that you can restore it if you make a mistake or results aren't to your satisfaction.)