Evan, here's my thoughts on your use cases:

Use Case 1:

-If you're looking for a report that could be scheduled to run every weekend that looks back over Timesheets submitted just in the past 2 weeks where the total hours for the Timesheets submitted during those 2 weeks is 0, then you could solve this purely through reporting. Do a report on the Timesheet object summarized by Person, with the Timesheet date range set to THIS_WEEK OR LAST_WEEK, or whatever makes sense depending on when your Timesheets have to be submitted by and when you want the report to be run.

-If, on the other hand, you want a report of ALL occurences of the rule "0 hours in past 2 weeks of Timesheets" over a much longer period of time (say over a month or semester), then I think yes, you'll have to set some sort of flag on the offending timesheets(s). I'd probably do the validation in the Save method of your Visualforce controller as long as Timesheets are being created strictly through the UI (i.e. none are created through the API), because it would be more straightforward to handle each Person's Timesheets individually.  Here's some sample code:

private Timesheet__c timesheet;

public PageReference save() {

	// Set a savepoint so that we can rollback
	// if anything goes wrong
	Savepoint sp = Database.setSavepoint();

	// Before we save this Timesheet,
	// check to see if 0 hours were recorded
	if (timesheet.Total_Hours_For_Week__c == 0) {
		// Get the most recent Timesheet for this person,
		// and see if 0 hours were recorded for it
		List<Timesheet__c> pastTimesheets
			= [SELECT Id, Total_Hours_For_Week__c, Date_Submitted__c
				FROM Timesheet__c
				WHERE Person__c = :timesheet.Person__c
				ORDER BY Date_Submitted__c DESC
				LIMIT 1];
		if (!pastTimesheets.isEmpty()) {
			Date lastSubmitDate = pastTimesheets[0].Date_Submitted__c;
			// If this was in fact the Timesheet for last week...
			if ((timesheet.Date_Submitted__c.daysBetween(lastSubmitDate) <= 10)
				&& pastTimesheets[0].Total_Hours_For_Week__c == 0) {
					// Flag the current Timesheet for later review,
					// but allow it to save
					timesheet.Flagged__c = TRUE;
				}
			}
		}
		
	}
	
	// Insert the Timesheet
	try {
		insert timesheet;
	} catch (Exception ex) {
		// Roll-back the database 
		Database.rollback(sp);
		// Let the user know what went wrong
		ApexPages.addMessages(ex);
	}
	
	// If our operation was a success...
	if (timesheet.Id != null) {
		// Send the User to the Detail page for our Timesheet
		// (or wherever else they should be sent)
		return (new ApexPages.StandardController(timesheet)).view();
	} else return null;
}

However, you could also do this through Triggers and future methods without using more than 2 SOQL queries, and with no danger of exceeding Governor Limits:

trigger Timesheets on Timesheet__c (after insert) {
	
	// We use an After Insert trigger because this way we know that the record
	// has passed all validations and has indeed already been inserted 
	if (Trigger.isAfter && Trigger.isInsert) {	
	
		Set<Id> personIds = new Set<Id>();
		
		for (Timesheet__c ts : Trigger.new) {
			if (ts.Total_Hours_For_Week__c == 0) {
				// We need to retrieve the 2 most recent Timesheets
				// for this person to see if they both had only 0 hours recorded
				personIds.add(ts.Person__c);
			}
		}
		
		if (!personIds.isEmpty()) {
			TimesheetUtils.CheckForSubsequentZeroHourTimesheets(personIds);
		}
	}
	
}

public class TimesheetUtils {

	// We run this as a future method
	// because it's not essential that it take place immediately.
	// If we ran it synchronously,
	// 		then the User might have to sit and wait longer
	// 		after pressing the save button on a Timesheet record.
	// Plus, we can't directly edit a record in an after Trigger
	//		--- i.e. we'd have to do DML in the Trigger,
	//		which wastes the User's time and eats at governor limits
	@future
	public static void CheckForSubsequentZeroHourTimesheets(Set<Id> peopleIds) {
		// Timesheets that need to be flagged
		List<Timesheet__c> timesheetsToFlag = new List<Timesheet__c>();
		
		// Retrieve the most 2 recent Timesheets for these People
		for (List<Contact> lstPeople : 
				[SELECT Id,
					(select Id, Total_Hours_For_Week__c, Date_Submitted__c
					from Timesheets__r
					where Total_Hours_For_Week__c = 0
					order by Date_Submitted__c DESC
					limit 2)
				FROM Contact
				WHERE Id in :personIds]) {
			for (Contact c : lstPeople) {
				// Verify that the two timesheets we retrieved
				// are indeed for subsequent weeks
				if ((c.Timesheets__r.size() == 2)
				&& (c.Timesheets__r[0].Date_Submitted__c.daysBetween(c.Timesheets__r[1].Date_Submitted__c) <= 10)) {
					// The most recent timesheet needs to be flagged
					timesheetsToFlag.add(c.Timesheets__r[0].Id);
				}
			}
		}
		
		if (!timesheetsToFlag.isEmpty()) {
			for (Timesheet__c ts : timesheetsToFlag) {
				ts.Flagged__c = true;
			}
			update timesheetsToFlag;
		}
	}	

}