If you're using a watch with an OLED display like the LG Watch R, Android Wear uses a mechanism to avoid burn-in when the watch is dimmed. The dimmed display will shift a few pixels every minute.

This means you should not place important information at the most outer border of your watch face. At least not in dimmed mode. Instead move it about 10 pixels off the border.

You should also try to avoid largish areas as these won't be protected from burn-in by the shifting mechanism.

An easy way to make sure the burn protection is effective is using an “interlace” effect on your dimmed screen. This can be easily achieved by putting a striped pattern above all your other layers and set it's Display property to “Dim only”. Make sure the stripes are solid black (only black pixels are truly disabled).

Example. Using this stripes.png as a dim pattern shows one pixel lines only: