Plus the fact that no unique constraints radically changes the optimizers choices for retrieving data. I'll bet you see a LOT more scans than you should since the optimizer has no way of knowing if your data is unique.

Honestly, I'd be hard pressed to list the very large number of issues you're seeing here that you shouldn't in terms of performance. But the biggest worry would be data quality. Your business can quite easily insert duplicate data if there are no constraints in place (and probably has). That would be the first, and most important, point I'd raise.