From reading the other question and comment you posted, I actually don't think you need to amend your return. Read this information below and see if it applies to your situation -
While you can agree to allow the other parent to claim the child as a dependent, only the custodial parent (one the child spends more nights with) can claim the child for Earned Income Credit (EIC), Child and Dependent Care credit (CDC), and Head of Household. You cannot "shift" those via agreement. You can, however, shift the dependency exemption and the Child Tax Credit.
So, if you answered the questions to indicate that you are the custodial parent then only you are entitled to the EIC, etc. Now, this scenario can cause problems with the e-file system because the child's SSN remains on your return in these scenarios as it is still your right to claim the EIC/CDC/HOH. What is happening is the IRS e-file system is hypersensitive (due to general ID protection measures) and it will still read the child's SSN on your return, even though you are not claiming the child as a dependent. And, thus, it will reject either your return or the other return.
The only way forward is the other party will have to print and mail his return. At this point, even if you were to amend your return to remove the child completely (and this could cause you to lose substantial refund if you are getting the EIC/CDC/HOH), the e-file system will not update in time this year as it can take up to 16 weeks to process an amended return. When he files by mail, the IRS will still process his return and pay any refund due, even though the SSN is on your return as it is legal. It is just the e-file system itself preventing him from filing.
Note: If you do decide that you want to amend your return, then no it won't cause issues. He can paper file his return and they will pay the refund. The IRS won't get around to matching the information until late summer, so as long as you amend your return in the next couple of months you will be fine. And, if you did get a notice, you would just respond saying that you amended your return already.