My son mistakenly claimed himself as an exemption on his tax return, but I need to claim him as a dependent on my return.

[milosamminouche]

I would like to amend his return, but I understand that the IRS takes several months to process 1040X forms, and I can't wait that long to file my 1040.

[ChelsiE2]

You are correct.  The IRS does take several months to process an amended return.  

However, you should include your son as a dependent on your return regardless of the error he made on his return.  Then you should paper file your tax return.  You will not be able to e-file as the return will get rejected.