The metal salts are too small to filter, even through whatman paper, so I just leave it in there.
I have found that the stuff that falls to the bottom is other things, that don't have the blackness of the metal salts. I think it might be FO, and also PO that has dropped out of solution. Most people use the PO hot, so you get a bit of concentration due to evaporation, and this might result in some crystal fallout on the bottom. If you do get large green crystals, add some distilled water, as you are getting supersaturated fallout.
I also get a very fine silt at the bottom that may be contamination from the paper that gets put through the developer, but I'm not really sure. It's white-ish and I thought it may be some carbonate buffering material.
I decant the PO when I pour it out, and always try to avoid pouring any solids on the print, as you never know what they will do to the image. The grains can cause some surface abrasion, at least.
Every once in a while, I'll run the PO through a coffee filter to remove all the larger sediment, and that's about it.