Until recently, Chrome 'implemented' the HTML5 date input by giving the user a spinner on the side of the input box which, when pressed, will set the date in the input to '00-00-0000'. Worse, this renders the normal feature detection used by libraries such as modernizr.js useless.
Text rendering is badly broken for Chrome on Windows right now. http://i.stack.imgur.com/MsHdy.png - Firefox, Chrome, IE9. Bug report: http://code.google.com/p/chromium/issues/detail?id=137692
There was a bug that caused inset box shadow used to be rendered outside the element. This is fixed in recent desktop versions, but still haunts older versions of Android's default browser - versions as recent as the one included with 3.x Honeycomb are affected.
Browsers, even modern ones, are incredibly quirky. Moving to a monolithic Webkit market will not help with any of the bugs listed above, nor, I suspect, most of the bugs one might encounter today as a web developer.