Bulk opening of several node edit screens
As far as I am aware, no module will do this out of the box. However in saying that there is a potential solution in:


Installing Views Bulk Operations (VBO)
Writing a custom action that happens on each selected node


From the VBO page:

How can I write an action that performs a function on all selected nodes AT ONCE?

You need to write a node operation instead of an action. Whereas actions get called once for every selected node, node operations are called once only, and they are passed an array of selected nodes. Check out sirkitree's article for the same concept applied to user operations.
Note: If you use Batch API to execute your actions, VBO will revert to calling the action once per node instead. This is because it doesn't make sense to batch one single action.