skipping slave errors should only be used if you know the problem that occured won't be of any problem for the rest of the replication .. the error tells you that there is already a record in that table with the same key ..
1. Do you have "read only" in your slave config?
2. Remember that a SUPER user is exempt for "read only" (they can always edit data on a read only server)
3. if you're sure you can continue do:
SHOW SLAVE STATUS;
and check if the "Seconds Behind master" field is decreasing..