I had same situation in 2005

CBP in LAX did't cross out my H1 entry, so I went back China again. I got trouble when I was passing China board. officer questioned me how did I entered USA last time when he checked my Passport and Visa. I explained that US CBP made mistake so I save the entry. He said he couldn't let me go because I didn't have vailid visa indeed.... Finally, we talked to the airline and airline agreed to take me. I wrote a guarantee letter said I would be responsible for all returning cost if I was refused by CBP.
It took about 2 hours to settle, I would've missed flight if the flight hadn't delayed.

It's very smooth when I passed CBP in LAX. CBP officer didn't asked any questions and let me in.