Quick disclosure: all of the tricks and tips below have been tested with CDT, but there's a chance they won't work with FireFox's Firebug Add-on.
The second debugging tool is fairly new to me. If you click on the 'Scripts' tab and choose one of the JS files included in the page, you're able to add breakpoints to the code by clicking on the line numbers. Once the breakpoints are added, you can step through every breakpoint. It can be tedious tracking down the code you want to put the breakpoint in if you have many files. It's especially painful if you're writing in CoffeeScript as the line numbers you're editing in your .coffee file differ from the compiled line numbers of the same .js files (what you see in CDT).
If you right click on any part of a website in Chrome (with the exception to a website built in Adobe Flash), there's an option called 'Inspect Element'. This is any front-end dev's bread and butter. You can view/edit HTML, traverse the HTML hierarchy, view CSS for any HTML element...the list goes on. For the most part, inspecting the HTML is elementary (yes, pun intended), but did you know that if you select an element, go to the console, and type '$0' - the last element you inspected is now tied to that variable? I didn't. Will User dropped that gem on me last week. The $ command dumps previously selected nodes, try typing $2, $3 and so on.
Here's another one that is news to me. There are certain CSS selectors that are used on every custom-styled button (or link). They are ':hover' and ':active'. If you have a button that is supposed to change it's image when you cursor over it or press it, you're invoking one of these selectors. It's a pain to style them though because when you hover over the element, the CSS properties show but you can't edit them without moving your cursor over to the CSS property (it's hard to explain, just try to do it and you'll see what I'm talking about). Enter the 'Toggle Element State' feature. In the CDT CSS pane, click the 'Styles' arrow and then click the button with the dotted square with a cursor in the center of it. Now you can toggle these selectors. See below:
Console DOM Tips
Lastly, let's go over some tips that involve both the console as well as the Document Object Model (DOM). Fire back up that console press (⌘ + K), which will clear the console. Grab an element off the DOM with jQuery (or do $0 if you've recently inspected something). Now call 'dir()' and pass in the element. As you'll notice, 'dir()' will print out every attribute/property that exists for the element. There are definitely some properties I didn't even know existed after using it for the first time.
If you have some CDT functions/tools/tricks that I didn't list, please share them in the comments.