I agree that my plugin, Standard Widget Extensions, might cause overlapping of a sidebar and a footer in dynamic pages. You could avoid this by calling swe.resizeHandler() at the end of JavaScript which manipulates contents.
But regarding your front page, it might not be caused by the plugin. I replayed overlapping without the Standard Widget Extensions when I use a Twitter widget from Jetpack in Twenty Thirteen. You could easily confirm this by disabling the Standard Widget Extensions.
For me, it seems that Twenty Thirteen with dynamic widgets also needs to be taken care after whole contents has been built.