Recently I noticed a weird noise, almost like metal scraping whenever the car moves. I have recently replaced the rotors and pads both front and back(both within the last 600 miles). Any ideas of what this noise could be coming from? I have an 05 350z with around 133xxx miles.

 

Probably a bent brake dust shield

 

Lots of things that could be causing that noise. Dust Shield being one of them.

1) Did you make sure you purchased rotors/pads matched for your specific trim package (Brembo or non Brembo or other BBK).
2) Did you make sure the brake hardware kit was installed properly so the pads are not dragging? (Spring clips properly installed).

Were there any other changes? Such as new wheels/tires? BBK upgrade?

The simplest explanation/cause is the dust shield. I've also had a small pebble or debris get wedged between the brake pad and rotor causing terrible noise under low speed/light braking. Do you have any witness marks or grooves forming on any of the rotor surfaces?
-Icer

 

As stated it’s most likely a dust shield, but it could also be an install issue with the shims/clips. Did you do the install or was it a shop? If you paid someone to do it I’d be going back ASAP, but if you did it yourself I’d be taking a look at your install ASAP.