First, there is a specific place on the Uniform Support Order for the judge to enter the start date of a child support order. It can be as early as the date you filed your petition for child support. Check there to see what, if anything, the judge wrote.
Typically a judge will include any verbal orders in the written order. An omission of a verbal "order" from the written order should have been immediately followed up with a motion for clarification, reminding the judge that she/he gave a verbal instruction but forgot to put it in the written order. The problem, however, is that there are time limits for filing certain motions that might have corrected this error. If your written order is dated June of 2012, then all deadlines have most certainly passed.
The problem with it not being written is that, if the next time you go to court you have a different judge, there's no way for that new judge to know of and enforce the verbal order. I don't even think the SAME judge could hold the other party in contempt for violating a verbal order.
Lastly, with respect to your second question, any violation of a court order is grounds for filing a motion for contempt. After filing a motion or petition for contempt, a hearing will be scheduled where you will have to present your evidence. The judge will make a ruling on whether or not the party is found to be in contempt, and if so, the remedy to bring that party back into compliance.
My office handles child support and other family law matters. We can be reached at 603-329-5200.
Note: This comment does not create an attorney client relationship. You do not have an attorney until you hire one and pay the requested fee.