If the file was flashed incorrectly due to a malfunction in the MK3, it should stop the flashing process with a "fatal error" on the upper screen. However, running an incomplete flash should not brick your DS, since most of the time games will not be writing to the firmware or firmware settings.
Try removing the MK3 and rebooting the DS. If that still gives you a problem, use the fail-safe to recover FlashMe. Oh yeah, if you are using Menu v0.5, remove the flash cart too.
Obviously, don't try running a game unless its completely flashed. Also, I noticed a little bit of play in my MK3 and DS connection. If I set the DS down on a flat surface, it kind of pushes up on the MK3 maybe half a millimeter. Sometimes this causes the flashing to fail. Try resting the DS on a game case with the MK3 hanging over the edge so nothing pushes up under it.