Unstored calculations do slow down searches and sorts as well as screen refreshes if you have a lot of them such as in a list or table view where you may display the same field many times. Whether this is a significant concern depends on the quantity of records involved and the speed of your system. (Single machine with a fast processor, shared over a LAN, over a WAN, using a Filemaker GO as a client....)
Auto-entered calculations do not auotmatically update if a related record's value referenced in the calculation is changed. That's the most critical limitation to keep in mind. In your situation, I suspect that the date is not being entered because the record in the related table where the date has just been auto-entered has not yet been committed. Commit the record via script or by clicking on a blank part of the layout first and then enter data in your line item record and see if that works for you.
You can automate the process with a script trigger that commits the record. You may have to play with different triggers to find the best option here though an OnObjectEnter or OnObjectExit trigger will probably do the job for you.
Once again right on the money.
I created a script that commits the purchase order record, then sets the field in the lines table which creates that record and allows the calculated value to work as I pictured it.
Take home message *Committing a related record must be done first* for a calculated value to work.