I recommend sampling the tailings effluent and river water to submit for ICP analysis. This will give you a better understanding of the metals present and your next steps. I think you need more information to be able to understand the impact on recovery.

You can also sample some slurry from the front end of your process, wash it, filter it, and then perform a leach test with clean/DI water compared to a leach test performed with the reclaim tailings water side by side. You can then compare the leach kinetics of both samples to see if the process water is decreasing recovery.

The above info is very good. If this is a cyanide leach you very well could have several different metals in your dore, especially if you are using zinc precipitation. Zinc tends to precipitate most everything below it on the electromotive chart. You can do a XRF on your dore and see what else you are picking up. I have seen it where if you are using your water over and over again you can have trouble as things build up in the water and you my need to periodically bleed off a portion and use more fresh than you are using at the present.    

Be careful not to dismiss the river water as a potential source of your problems.  Particularly in northern climates, river water chemistry changes with the seasons.  Look at TDS levels and pH.  Also look at what happens when you mix the two.  I would suggest you run several parallel tests, one with clean/DI water, one with 100% recycle solution, one with 100% river water, and one with a typical blend of recycle water and river water.  Your ability to bleed off water and use more fresh water is a function of regulatory issues, the cost of fresh water, and the cost to discharge or evaporate tailings water (including treatment costs).  Don't worry too much about what is in your dore, work out how to maximize gold and silver recovery first.  Good Luck - it sounds like an interesting project.