Video problems:

Atari Falcon / TOS v4 compatibility bugs:
  When running some versions of Hatari (including 2.3.0) in Falcon
  emulation mode with NatFeats support disabled, you may see the
  following message (or similar) on the Hatari console when EmuTOS
  switches to monochrome mode:
    WARN : Strange screen size 160x400 -> aspect corrected by 4x1!
  This is because of the method that EmuTOS uses to bypass a potential
  Falcon hardware problem (see the relevant code in bios/videl.c), which
  puts the screen into a nonstandard resolution for one frame.  This
  method works without problems on real Falcons, and the message may
  safely be ignored when running under Hatari.  Note: you will not see
  this message if NatFeats is enabled, because EmuTOS then knows that
  it is running under an emulator and will not attempt to bypass the
  Falcon hardware bug.

Problems that also occur in Atari TOS:
+ BIOS: Startup time can be slow on a floppy-only system.  You can speed
  things up by ensuring that you have a formatted floppy diskette in
  drive A at boot time.  Boot time will be further reduced if the root
  directory of the diskette contains as few files as possible, and there
  are no "deleted file" entries in it.  This can be achieved by freshly
  formatting the diskette and then copying any desired files to it.
+ VDI: when drawing a wide polyline with squared ends and more than one
  segment, if the width of the line is greater than twice the length of
  an ending segment, the end will have a bump rather than being square.
  This is because wideline segments are joined by using filled circles
  whose radius is half the width of the line: the bump is a protruding
  part of the circle that joins the end segment to the previous one.
+ RAM: Cold boot may not be properly detected on some configurations. This
  may happen if the computer has been switched off and on too quickly.
  In that case, the welcome screen is not displayed.

Links to programs listed above:
