This is due to some changes between earlier versions of dojo and version 1.6.1. Version 2.3 of the ArcGIS API for JavaScript uses version 1.6.1 of dojo and in that version if you have a child of a border container without a region attribute specified you may get the 'word is undefined' error. You can fix this by specifying an region attribute.
http://bugs.dojotoolkit.org/ticket/12795
Chris,
I haven't experienced issues with absolutely positioned divs at 1.6. If you'd like to post the code you are having problems with I'd be happy to take a look?
One thing i did to workaround this is to put all the other none region divs within BorderContainer's region ContentPane such as mapGallery in map ContentPane (region="center") etc.