As Bsch4477 said, it's possible that your ex would be subject to penalties for claiming the children when he wasn't entitled to in the previous years.
However, going forward, as long as he gives you, the custodial parent, the form 8332 to sign, which gives the noncustodial parent, namely: your ex, the right to file the dependency exemption, he should be entitled to claim the exemption.
I don't see anywhere in the IRS codes or tax laws indicating that this affect him negatively in his future tax filings if he follows the proper guidelines subject to court / IRS rulings.
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