My guess would be slugs. There must be a better environment for the slugs on the side with the damage than on the other side. Look for places where they can hide: under mulch or debris, under rocks or boards. Note your watering practices - slugs like wet environments. You can verify it is slugs by laying down a board overnight to trap some. Also look for slime trails.

There are many (some successful, some not so much) control options. Read here:
http://www.extension.umn.edu/garden/insects/find/slugs/