I ordered new checks and instead of my zip code being 96744 it's 967444. So there's an extra 4. Is this a problem?

It isn't a problem. What's important is the routing # of the bank and your account # at the bottom of the check. Just cross out the extra 4.

So contact the bank or check printer and request corrected checks.

Yes, your checks are no good for use. Shred them and order new ones.

The account number is on the bottom of the check, that is all that really matters.

Not a problem