on many faucets, there is a metal screen on the input. This is to prevent any chunks from getting inside of the valve and messing with the seals or blocking things off. It is better to catch it prior to the valve than within it! So, it seems like it may be those screens a clogged. If you can find a parts list diagram for your faucet/tub filler, etc. maybe on the web at the manufacturer's site, it will give you an idea if there is one. On the faucets say at the vanity, there is also a screen on the aereator which, if clogged, will affect the flow. From what I read, the tub filler should flow in the area of about 6 gallons/min (that's just approximate - depends on pressure, and other things). The showerhead (if new) is maxed at about 2.5gpm. Some tub/shower valves could show this effect if the internal seals are bad.
How old is the tub fixture? What brand? Do you know the model?
Galvanized pipes become clogged, eventually, you'll need to replace them.
Note, I'm not a pro.