Check to see if you are using an Interlace screen mode.
Agreed. Petercli: change your resolution to a non interlaced mode. As Danbeaver has pointed out, the guy in the video uses an additional bit of hardware (Indivision AGA MkII) to de-interlace the display and convert to a format suitable for modern monitors. As you don't have this, don't select interlaced modes unless you want a headache!
