Maximize window (Firefox or Safari)

You'd need to use a Bookmarklet such as this one, and save it (or move it) to your bookmarks bar. Then you can just click it once to maximize the window to the size of the screen.

Just create a new bookmark from any page, then change it's name to something like "Full" or "Full Size", and in the URL portion, enter this JavaScript code:

javascript:self.moveTo(0,0);self.resizeTo(screen.availWidth,screen.availHeight);

Once you've done that, it should work fine, though you may need to restart Safari before it recognizes the fact that it's there.

I don't have that problem except with iTunes, and since my Dock is on the right-hand side of the screen, there are a few rows of pixels (2 or 3) it will not expand the window into.

Mac OS X is the most advanced OS, but it could very well be that it has determined the available screen width/height to be something other than what you think it should be. It could be the true dimensions of the screen based on the size and viewable area, even if you see an image on those few rows of pixels. Any other OS would not necessarily be calculating the true dimensions of the screen, so assuming that Mac OS X is automatically at fault is presumptuous at best.

If you are game for a 3rd party approach to full screen, install Glims. Once installed, you'll find Glims' preferences as a separate panel in Safari Preferences. There, you can activate Full Screen.

When you are ready to use Full Screen, simply go to the Safari Menu and select it.