I plan to use them on everything moving forward!
Good for you! Starting with valid markup is the best way to ensure good cross-browser displays. with regard to the CSS errors, you can ignore the -webkit & -moz ones. Although, strictly speaking, they're not valid CSS, they shouldn't cause any issues in other browsers. The "value error" ones are the most significant and I'd also suggest checking out the "empty string" errors too.
Once they're all sorted, if you're still having problems then it will be down to a flaw in your CSS "logic" - widths, margins etc. Or the fact that something inside one of your main content blocks is pushing the block wider than you intended.