Thanks all. Here's an answer from Shotgunworld that I think sums it up well:
Receivers serial numbered post 855,000 accept the interchangeable barrels. If you find a barrel with a serial number on it, it will not fit into the post 855,000 serial numbered receivers. Also, a receiver serial numbered pre 855,000 will not accept an interchangeable barrel. When you buy a pre 855,000 gun, be sure that the serial numbers on the receiver and barrel match.
The Ithaca Gun Company on their website recommends the head space be checked on every barrel installed on a receiver. You should read their website in regards to this. In today's litigous society, I suspect that is somewhat for legal defense purposes. However, you might come across an interchangeable barrel that should fit into a post 855,000 receiver but won't. I've had this happen to me once. Also, I tried to put one older interchangeable barrel, made in Ithaca, NY, onto an Ohio made receiver, and it was a no go. Perhaps because of the extremely tight tolerances the new Ohio made 37s have due to their CNC machining, I may have to restrict my Ohio made barrels to my Ohio made receivers.