I got a contract back signed by the Client and he also signed on the part where our company's director is supposed to sign. It won't let me correct it, so does that mean I have to cancel the whole thing, or can the client correct it on his end?

This is easy to replicate. I created a new envelope, added two signers, when I dropped tags I added the Signature of the first signer to the area for Signer 1 and Signer 2, not setting the tag color correctly for Signer 2. So when I send, then Signer 1 must sign both places to complete the envelope. Now Signer 2 has no location to sign. You cannot correct the envelope because you cannot remove Signer 1 nor remove Signer 1 signature blocks cause they already completed.

The only option is to "Void". BUT after you void, go to the original Sent envelope and copy it, then it will contain the same document, Recipients, email body and subject, but make sure to adjust the Signature Tags to the right color and Send.

Using copy saves a little time.