Despite using a fine mesh strainer, when I pour out my stock into a container, I appear to have a lot of sediment/debris in my stock. I am following the method used by Chef John (Foodwishes) http://foodwishes.blogspot.com/2012/02/roasted-chicken-broth-part-1-of.html and I'm not sure if this is normal, or if I should be doing more to get a cleaner/purer chicken stock. I do my best to skim, but as a newbie, it's hard to tell if I am skimming the right parts.
A stock made from roasted chicken is never going to be clear like a consomme.
You will note in the the video you reference, the stock is also moderately cloudy with some particles floating around in it.
This is normal, and nothing to worry about.
If you do desire a more clear stock next time:
In truth, I would suggest this is not worth it for most applications, unless you feel the appearance of the final dish being created is marred. Since aspics are no longer terribly popular, where a clear gel really is needed for appearance, normally getting a very clear stock is not needed.