I've got a View of 10 images displaying inline, the first and last images are different (have rounded corners), and it is really important that the order for all 10 images is locked in. Is there a way to do this, without having to edit all the nodes in order to get them displaying in the correct order?
You want the Nodequeue module.
You can make a queue and add nodes to it an arbitrary order. All queues have an associated view that gets created, and can be used anywhere you use a view.