Hmm, I think I know what you're talking about. If it sounds like the brakes on a car squeeling, it's possible that it the laser's focus coil is pushing the laser lens too high, causing the lens to scrape on the bottom of the disk as it rotates. Check the bottom of the disk to see if it's got scratches that go in a circle, that'll tell you that it's probably the laser lens.
If it's quick, and only happens every so often, it could be the laser moving along it's slide as it goes from the inside to the outside of the disk, and back again. If that's it, and you're comfortable opening up your PS2, I'd suggest you put a bit of white lithium grease on the 2 rails the ps2's lens slides on. That hopefully should fix it.
As for a fix for the first one, I don't have a clue.
Anybody else have any ideas?
Model: NTSC SCPH-39001/R (think it's a v7)
Mod: PS1 Exploit Softmod
Harddrive: Internal 40GB Seagate ST340810A
External drive: Apple iPod (in Disk Mode)