The problem is that the MacBook display only has a resolution of something like 1440x900. I forget the exact resolution, but it's just barely over 720p. If you're mirroring the displays, that means OS X (Windows, and pretty much every other OS) is going to apply the same resolution to both displays.
If you want to use the MacBook with the external display, not the internal display, then when you boot the MacBook you need to close the clamshell just after the boot chime. This should force it into using the external display only. Otherwise, it's going to try and find some way to reconcile the fact that the two displays have different maximum resolutions, and as you can see, the results aren't pretty.
Alternately, you could just set up an extended desktop, set the external monitor as the primary display, and then simply ignore the internal display. Which would be a far simpler solution, if a bit less elegant.
I have a MacBook Pro (purchased Dec 2010) and have just purchased a ViewSonic monitor (model VX2453mh-LED)...it's 1080p full HD. When I connected the computer and the monitor with HDMI cable and adapter, and mirrored the displays, it defaults to 1080p in the resolution selections, which works "ok" but the display is too big vertically (I can't see the top menu bar, and the dock at the bottom is only half visible)...it actually doesn't fill the monitor screen horizontally (approx. 1/2 inch on both sides), which isn't a big deal.

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