I missed checking the box on my own return that I can be claimed as a dependent by someone else. How do I fix it when my return has been rejected?

Yes, you can change it if the return was rejected. 

Go back into his tax return.

1. Under My Info (Top of left sidebar)
2. Click the down arrow next to his name
3. [Revisit]
4. Continue to Let's check for some other situations
5. [X] Another taxpayer can claim me as a dependent on their tax return.
6. Close the return and re-tile it

If you were rejected for something other than this, you must also make that correction.

Click your name in MY INFO and go back through the screens to the question about whether you can be claimed as someone else's dependent and change your answer; then try to e-file again.