[Update] we've seemed to solve (at least temporarily) the cloudiness when the water is cold (we flushed the whole system from top to bottom), but now I'm seeing it exclusively when the water is hot. The noise continues. I'll also mention that:

a) our pipes are all copper (and not plastic as I observed in our previous place)
b) none of our kitchen or bathroom faucets have shut-off valves
c) the water pipes visible in the basement have a significant amount of 90 degree angles in the system.

I just purchased a home (13 yrs old). The water out of our taps is coming out cloudy unless we trickle the tap. The cloudiness clears up in less than a minute, so we're pretty sure it's air and nothing more sinister, but our pipes are also quite loud if we use the shower or the laundry tub (at the top and bottom of the system respectively). I was going to flush the system from top to bottom to try and solve the cloudiness problem, but I'm concerned that the loud noise is possibly hammering which I understood was caused by a lack of air cushioning.

Any advice would be appreciated before I bring in a plumber. Thanks!

Try putting on new aerators on the sink faucets for the cloudy water problem. It may not solve the problem, but they are cheap and easy to replace, so its worth a shot. As far as the loud pipes, most likely the pipes were not securely anchored(judging from the fact that there are no stops on the sinks, I doubt the work was done by a licensed plumber). One option here may be to install an expansion tank on the water system to see if it helps reduce water pipe noise.