I can confirm the same problem on one of our sites. I setup a workflow email to send me a notification an order was submitted along with the ship type because we have been having shipping problems.
* The shipping method says "Standard delivery" (I'm not sure how they could get this as an option?)
* There is no shipping amount listed at all.
When in the admin area I can click "calculate shipping" and it displays the correct flat rate option.
* UberCart Coupon Module 5.x-1.3
* Ubercart rev 1228