There are so many issues to do with portability and compatibility that unless you are doing something very simple, its is an amazing achievement to get your web page to display even remotely similarly on several browsers or platforms.
Leaving aside the creative issues to do with color matching, gamma correction, and display resolution, there are problems with fonts, stylesheets and table layout. Layers and dynamic HTML behave differently even within the same browser family as the browsers are revised. Even scrolling a page means you have to increment the scroll value in opposite directions in Netscape and MSIE, and Netscape won't scroll at all without the scroll bars being visible.
To cope with this, it helps to break the compatibility issues down into sub-sets and to understand the underlying reason for incompatibility. You do need to know about and be able to identify issues based on platforms, browsers or versions of client software.