Q - Under what circumstances could the order date not match the order entered date? Below is an example. To us, it looks like the entered date should be 5/25/16.  See sample screen below:

A - The Order Enter Date is always the system date (the date the order is created) and the user has no way to override it. The Order Date by default equals the system date. However, the user can override it. Go to COP -> Inquiry -> Line Item Auditing Inquiry -> Inquiry -> Audit Inquiry by Order, and enter order# 378803. Then you will see that the line items for this order were  added on 6/1/16. Also, if you bring up orders # 378802 and 378803, they are all entered on 6/1/16 with order dates of 6/1/16.

This proves the order was entered on 6/1/16, not 5/27/16. I think the primary intention in overriding an order date to an earlier day is to get an expired sales price. In this case, we don’t clearly know the motivation behind this overriding of the order date.

Just FYI, we did introduce a new flag in Global Setup -> Cop-Func -> Order Line Item Screen.
    34. Price Date Used When Add Item To Exist Ord?
If you choose "S" (System Date) for this flag, then the price is calculated based on the system date instead of the order date during order entry change mode.  As for order entry add mode, it is always calculated based on order date.

EMK