Remember that contract? It's a binding agreement between you and your contractor that spells out exactly the work to be done. If you notice that work specified in the contract is being done differently, shoddily, or not at all, it might be time to fire your contractor in favor of one who'll get the work done right.
This includes not only how things are made, but what they're made of. Your contract specifies the materials to be used, but you can bet there are cheaper alternatives. The price difference between the contracted materials and the knock-offs the contractor buys would go directly from your pocket to his. So consider non-contract, substandard materials a version of theft and treat it accordingly.
The same is true of cutting labor costs. If you've contracted for a certain amount of labor-intensive stonework, you should get exactly that amount. A contractor who slights the contract slights you.