Is there a way to force execution of all validation rules?

I don't think there is any out-of-the box way to do this. Maybe you can quickly do this with some anonymous Apex code:

List<Opportunity> failingOppys = new List<Opportunity> ();
for (Opportunity o : [SELECT Id FROM Opportunity]) // Here you should select all fields that may cause validation
{
Opportunity ocl = o.Clone (false, true, false, false);
try {
insert ocl;
delete ocl;
}
catch (Exception e)
{
failingOppys.add (o);
}
}
System.debug (failingOppys);
This code is non-bulkified so you may hit some Apex limits after 100 records or so. Let me know if this approach could work for you and perhaps we could come up with a bulkified/batched version of it. How many opportunity records are we talking about?