Tax question..My ex wife and I have joint custody...Who gets to claim the kids on their taxes?

Whoever the child actually stays with for over half the nights of the year is considered the custodial parent by the IRS, and gets to claim them unless there's a court order that specifies otherwise, or unless that parent signs a form allowing the non-custodial parent to claim them..

No, no, no, go count the nights where the kid has been sleeping. Whichever parent had the most nights has custody and the parent with custody gets to claim the child on their taxes by default.

You the court decree didn't specify one of you and neither of you kept track, it's going to be a little difficult to figure out.

Generally the person that has the kids for 6 months or more gets to claim them. So if you have joint custody and you have the kids during the week and she has them on the weekend, then you can claim them. If you have equal custody (like split weeks or one month on/one month off) then you have to discuss and agree on who gets to claim them. Check your divorce papers, this is very often outlined in the settlement.

There are a number of exceptions and special rules in the tax code, so without knowing the particulars, it appears that Internal Revenue Code ("IRC") section 152(c)(4)(B) sheds the most light on your problem:

152(c)(4)(B) "More than 1 parent claiming qualifying child."--If the parents claiming any qualifying child do not file a joint return together, such child shall be treated as the qualifying child of--
(i) the parent with whom the child resided for the longest period of time during the taxable year, or
(ii) if the child resides with both parents for the same amount of time during such taxable year, the parent with the highest adjusted gross income.

But also see the IRC regulations at section 1.152-4T ("Dependency exemption in the case of a child of divorced parent, etc."), which also includes explanation of general rule described above, but outlines scenarios where the parents may, by written agreement, deviate from that rule.