Anchoring too aggressively. If you make a first offer way outside of the ZOPA, you may have to make large concessions to reach a deal or walk away even though a zone of possible agreement exists.
Anchoring too conservatively. You unknowingly give away a big chunk of the ZOPA on your first move.
Use the midpoint rule to your advantage in the first offer itself. Think about where you want to end up and start with a counteroffer that gets you to that number as a midpoint.