Confirmed for Minecraft 1.9
Looking at the NBT data of level.dat, it does appear 'BorderDamagePerBlock' is being updated after typing "/worldborder damage amount 0". So the command itself appears to be working at that level, but the game itself is ignoring the "0" value, and continues to damage players.
Entities like mobs don't appear to be taking damage.
Thanks! Sorry for the duplicate - I did a search for the error message rather than the cause of the issue, and didn't see it.
Have tested again in 14w31a, but still no luck.
This issue has been marked as resolved, however is not resolved. Affected versions has been updated.