Do you have Berkey PF-2™ Fluoride and Arsenic Reduction Elements? If so, run a batch of water through the system without them attached. If the water runs through clear, we know that the PF-2s are causing the cloudiness. If the water is still cloudy, we know that the Black Berkey® Elements are the source.
If the Berkey PF-2™ Fluoride and Arsenic Reduction Elements are the issue, re-prime the elements from both sides to force out any residual media from within the filters. If you have over-tightened your Berkey PF-2™ Fluoride and Arsenic Reduction Elements, you may have damaged the screen on the inside which keeps the media from leaking into your system. This is not covered under the 6 month limited warranty for this product.
If the Black Berkey® Elements are the problem, clean/re-prime them and perform a Red Food Coloring Test. If the test passes, contaminants are being removed properly and the cloudiness is most-likely healthy minerals. If you are using softened water on the elements, this could also cause cloudiness. You should not use softened water on the Black Berkey® Elements.