Wow. And I had no idea that this thread existed!
Actually this is a problem with how docking boxes (the feature that lets you drag and drop, expand and collapse etc) can be tied in with WordPress widgets (I am the theme creator, BTW). I have explained this problem a bit here: http://www.aquoid.com/news/2009/10/issues-with-nextgen-widgets-on-suffusion/ .
The short of it is, if the widget gets printed without a title, it doesn't remain a part of the "docking boxes group". Note that I say "printed", not "created". A widget's author controls if and when to print the before_title, 'after_titleand title elements. The default implementation of the "text" widget doesn't print thebefore_titleandafter_title` elements if the title is blank, but all other default widgets print these elements even if the title is blank. This was actually causing large-scale breakdown of the layout upon using text widgets without a title. I fixed this issue by overriding the default text widget, but the problem still remains for widgets based on the default text widget.
Here is some more information. As a part of the "docking boxes group" a widget's position, expand/collapse settings etc are stored for your browser. So you might have done some positioning at one point in one browser causing the widget's position to be erratic when you add subsequent widgets. That is why when you load it onto other browsers (where you haven't moved the widgets around) you are fine.
There are quite a few fixes for this:
1. Do as Greg suggests and disable docking boxes by disabling drag and drop. This will fix widget positions based on your admin panel. Note, though, that if you are using a widget that doesn't print the title, you might still be breaking the layout.
2. Or define a title for the widgets - this is always worth a try and for most cases (but not all cases) it lets you have your layout and drag-and-drop as well.
3. If you are concerned about the widget positions being inconsistent across different browsers, you might want to delete your cookies and test it out again - that is how a new visitor will see your page.
Please note that this is not related to CSS and positioning at all. The fact is, WP provides a before_title and after_title, but not a before_content and after_content. That would have really made things a lot easier!
A note to myself - I will avoid docking boxes in my next theme. It is not worth the pain.