Sure sounds like your chimney is a good candidate for a re pointing job. This involves removing all loose and damaged mortar, then pointing all the joints with a portland cement mortar. If you have never done this kind of work, read up on it. It can get quite involved if there are loose bricks etc. It may be a good idea to get a pro, so it will last awhile and not just fall out as soon as it dries. An alternative product for a quick temp fix can be found in a caulking tube. There are several products designed specifically for masonry and do a pretty good job in sealing small cracks. Remove as much loose mortar as you can to assure the masonry caulk sticks well.
I would venture a guess that @Tester101's suspicion about your floaties coming from your glass (unrinsed soap, dust, etc.) may be heading down the right path. I would try rinsing a glass, scrubbing it with a new sponge or clean washcloth, wiping it dry with a clean towel (not paper towel, as this may leave pieces of paper behind), and then refilling it. @NiallC's comment about asking for a water report from your municipal water supply is a pretty good alternative, but doesn't factor in anything that may come from the pipes between them and you. Most health departments will do water testing, so you could always fill a bottle and take it in.
Beyond that, if you really have to know what's in the water, your only real solution to absolutely know with 100% certainty (technically, unless you watch the health department do the tests, and can verify their results, you can't KNOW that they're right...but I'd probably just accept it) is to get testing kits for this, that, and the other thing (that was just the first page offering a wide range of kits that I found), that operate similar to what you might use for pool water. Depending on the sensitivity levels, you may pick up on things like trace amounts of chlorine...but of course this is going to get back into the more expensive end of things, as those kits aren't cheap (Grainger's seem to run around $40-$50 and up...it's about $20 for their cheapest, which is testing for copper, on that first page of results).
You could pick up a pool test kit, which will cover a couple of parameters (chlorine, calcium, hardness, etc.), but it's not going to cover everything and may not operate in the range you need to identify your floaties...it's designed primarily to help you maintain clear-looking pool water that you're not drinking, not crystal clear tap water.
So really:
Ask for report from municipal water supply
Take in sample to health department
If you're still paranoid and want to know what it is, buy test kits
If you just want to get rid of the floaties, filter, filter, filter, and make sure your dishes aren't the source
Best Answer
I would just take one of the old ones with you to a home improvement or plumbing store and find a close match.
If you are trying to order them, you need to measure the outside and inside diameter along with the thickness.
Sometimes it is necessary to stack two of them if one set of threads is not that deep and doesn't make contact with the washer even when it is fully screwed in. In this case, adding a second washer ensures that the shower head makes contact with the washer and creates a proper seal.