As important as it is to hide certain elements (such as navigation, searchbox, etc.) from the dialogs, there are elements you should not and cannot hide, but that can cause problems when the web page design (e.g. min/max widths and heights) are suddenly implemented in the dialogs too. For this, SharePoint 2010 didn't have any absolute and really good way of fixing. But SharePoint 2013 does.
Use the class .ms-dialog as the parent class for any rules you want to use for certain elements when appearing in the dialog. For example:
min-width: 0; /*as opposed to e.g. a setting of min-width of 800px*/
It still isn't perfect, but much better than before.