Thank you for contacting Ask Extension!  Although it is possible that the brown tips and spotting in the close-up photos may be caused by pathogens or insects, the most likely cause of overall yellowing is a problem with soil moisture.  Hemlocks do best in moist, but well-drained soil, and will turn yellow in response to very wet or very dry soil conditions.  In the photo, it appears that the tree is heavily mulched, which provides many benefits, but could also be preventing the soil from drying.  If the soil is remaining wet, the mulch should be removed to help the soil dry out.  You may want to carefully dig down into the roots with your hands and see if the roots look healthy.  Check the roots within the top few inches of soil.  They should not be mushy or brown, and there should be plenty of fine feeder roots.  If the soil does not drain well, the tree will not survive in this site.

For a small fee, you may have the needles evaluated for pathogens and the roots checked for health.  Bring a few small branches with the browning on the yellowed needles (as in the photo) and a small section of root (several inches, especially any that don't seem healthy, please keep moist) to the Washtenaw County Extension Office.  Please call or email for drop off dates and fee information.