[whpalmer4]

Is it important that Bill only get one email showing newly assigned tasks, or is it okay to send him an email showing all of his currently assigned tasks?

It is straightforward, though a bit tedious, to produce a report showing all of the assigned tasks for a given resource. Put a filter on the plan with View->Filter Tasks... with a rule that only matches tasks where the resource is used. Then, use File->Export... to export an HTML Task List. Mail the resulting file to the appropriate person.

There is a potential complication with such lists: they do not show dependencies in a particularly useful fashion if the prerequisite task is assigned to a resource not shown in the document. You get a column in the table showing dependencies by WBS ID, but if the prerequisite is not in the table, the resource just knows that the assigned task is dependent on some other task, with no clue as to what that task might be. I've attached a sample below illustrating this issue.

You could also set up Publish actions that would put the tasks in a calendar for each resource. I'm not familiar with all this new-fangled calendar sharing stuff, so I can't comment much about this.

One could also make a fairly straightforward Applescript that walks through the document looking at each resource, assembling a list of tasks assigned to each resource, and emails the final result. Might be easier than attempting to automate the use of Omni's reports, which is a sad state of affairs, I think! It does seem like a fairly obvious use case, but using the Export... approach to produce individual reports for all the resources in a plan is rather clunky, in my opinion, and the Applescript dictionary doesn't give much hope for automation.