No major browser has implemented CSS1/2 in its whole. Certain things, like a hover for links work just on one of the two major Win browsers. Microsofts IE4 has a rather good CSS implementation, but some things still won't work, like an initial letter. Here I'll list some bugs, problems or incosistencies among browsers, plus the workarounds if I know of one. If there's no workaround given then I need your feedback.
NN4 bugs
Width
Bug
Workaround
Set the elements border to 1px.
Relative paths
Bug
MSIE4 will look for the file relative to the position of the stylesheet, while NN4 will look for it relative to the HTML file the stylesheet is linked from. One obvious way to escape the bug is to put the stylesheet in the same folder with the content. But this would mean you cannot use folders anymore to structure your files.
Workaround
Put the stylesheet not in the same folder as the content, but in the same level. For example, you have some files in folder "newfiles" and some in folder "oldfiles", but you want the included HTML files to share the styles. You'd put a folder "style" in the same level with a stylesheet and refer to it from the HTML files inside "newfiles" and "oldfiles" as "../style/screen.css". Inside the stylesheet, for example to refer to a background-image inside the "style" folder, you could now write background-image: url(../style/back.gif). See path sample image.
Font size
Bug
Also, if you use relative (percentage) units for headers, the one browser will use it relative to the headers original size, while the other browser will use it relative to a normal text size. Another problem is that even absolute font-sizes will look different on certain systems (like smaller on Mac) or even certain browser on one system (like NN4 Win will be smaller then MSIE4 Win).
Workaround
Don't use relative font-sizes. If you have to set one heading size, set all other h sizes as well to keep proportions. Try pixel units for fonts.
Transparent backgrounds
Bug
List indention
Bug
You could of course set the margin-left to a negative value, but then it would look bad in MSIE4.
Workaround
No real workaround, but since NN4 can't display list-style-images for some situations it helps to use negative margin and correct this with a list-style-image the width of the negative margin.
Resizing
Bug
Workaround
No easy solution, but there's a JavaScript workaround at WebDeveloper (see Webdesign links).
JavaScript
Bug
Unknown tags
Bug
MSIE4 Mac bugs
Style media
Bug
Workaround
First link to the media print, then link to media screen and revert all print settings within the screen styles, like if you hide all online banners for print, use .onlinebanner { visibility: visible } for screen.