When a floating box appears directly after a header in Mozilla, the very first line of text after the float doesn't obey the float but is rendered right through the floating box.
The first floating box on a page is never affected by this bug, though.

Test page. Workaround is not included.
Reported by ppk.

Opera doesn't accept a cursor: pointer for an input type="submit".

Test page. Workaround is not included.
Reported by ppk.

Explorer positions a background-image underneath the border of the element. Therefore it's impossible to get the position of a background image in an element with a border correct in all browsers.

Test page. Workaround is not included.
Reported by ppk.

When using multiple class names for an element, Explorer will ignore all but the last of class names:
element.class1.class2 { }
Explorer completely ignores the class1 selector and happily applies the rule to an element that has only class2 set.

Test page Workaround is not included
Reported by: Tino Zijdel.

Mozilla and Opera split up one huge text node into several smaller text nodes. Explorer Mac acts weirdly.

Maximum text node sizes:

• Mozilla: 4K
• Opera: 32K
• Explorer Mac: 64K (?)

Test page. Workaround is not included.
Reported by ppk.

Anchor (or "#name")links don't work when the target anchor is inside an overflowing element.
Solved in Opera 7.60p3

Test page Workaround is not included
Reported by: Sander Grendelman.

In IE with SP2 if you a few a few anchor tags for a menu that have some vertical distance from each other (by using the bottom margin) and on hover want them to change background color, you are in for a nice surprise (removing the margin of the anchor 2 places behind it ..)

Test page Workaround is not included
Reported by: Petrioli Gabriel.

When more than one animated GIF features on a page, Safari sometimes does not play the animation.

Test page. Workaround is not included.
Reported by Nic Rodgers.

Setting an inline border style (element.style.border) works in all browsers. Removing it to allow the normal border styles to return, however, is tricky in Explorer Windows and impossible in Safari.

Test page. Workaround is included.
Reported by ppk.

Mozilla doesn't honour a position: relative on a table, which can therefore never serve as a container for absolutely positioned elements. This is a deliberate choice, and not a bug, oddly.

Test page. Workaround is not included.

On the other hand, Explorer Mac behaves as if every table has a position: relative. It always positions absolute layers in the table relative to the table, even if they should be positioned relative to the browser window.

Test page. Workaround is not included.
Reported by ppk.

Setting up a row of floats in Explorer 6 can lead to a plethora of erratic behavior, namely duplicate characters; in this bug report, I go into detail on some pure-CSS triggers which can make these extra characters appear, examples on how the bug is triggered, and different ways to combat it.
Note that these bugs are not caused by comments in your XHTML, as is the well known original Duplicate Characters Bug.

Test page Workaround is included
Reported by: Agent EQzE.

When a floated box does not have non-floated content alongside it that extends the full height of the float (including its vertical margin), the next 'cleared' div after the float has a top padding that is twice what it ought to be (in IE5.5 and 6).

Test page Workaround is included
Reported by: Luke Plant.

Absolutely positioned elements have a secret right and bottom margin of 15px. When you place such an element flush right or bottom, an unwanted scrollbar may appear.
Possibly the margin is the space reserved for the element's scroll bar.

Test page. Workaround is included.
Reported by ppk.

When resizing a window vertically through resizeBy, Safari seems to move the entire window instead.

Test page. Workaround is not included.
Reported by ppk.

When seting class names dynamically through JavaScript, Mozilla doesn't apply the first-letter and first-line styles.

Test page. Workaround is not included.
Reported by ppk.