I've got this buzz coming from the bridge and it is from the saddles being loose. I tried to to adjust them one way or another, but it doesn't make the buzzing go away. Also, it doesn't really help me fix minor intonation problems. It's like the saddles do nothing at all, except from causing the buzzing. What should I do?
If its the type of TOM that has a retainer wire, its probably that wire rattling against the screws.

Adjusting the intonation might take quite a few turns of movement in order to make a significant change. Lift up the string and put it back down on the saddle again after you've adjusted it.
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Quote by Axelfox
When you set the intonation, first set each string (as you go, not all at one time) a bit sharp, (too short) so when you make the final adjustment the screw is being tightened, and therefore pulling the screw head against the bridge. That should make sure the screw is held firmly in place and can't vibrate.

If the screws are not doing anything, it's possible you have the type with a wire but the wire is missing. If I remember correctly, the wire is what retains the screw and keeps it from backing out when you loosen the screw to make a string longer, so the screw is just moving back and forth but not pulling the saddle. You may have to pull the string off the saddle, make the adjustment, make sure the screw is pushed against the bridge, then replace the string and tighten the screw a tiny bit to keep some tension on it.

The type without a wire has a shoulder on the screw that holds it against the bridge no matter which way you turn it. If it's that type, do the same thing, make your final micro adjustment a tiny bit of tightening so the shoulder of the screw head is pushing against the bridge. That will be also pulling the saddle toward the screw head, meaning it's basically in a bind between the two, and under enough tension it shouldn't vibrate.

Check the height adjustment posts too, they should be pushing upward against the bridge for the same reason. Don't lower it and leave it, lower it a tiny bit too far then raise it slightly to be sure you have a solid base for the bridge to sit on that can't slip under use.

This is the same thing I do when tuning, I never tune down to the pitch I need, I tune below it and back up, so the tuners are always under tension and can't slip and let the string go a bit flat. Any screws on the bridge should be done the same way. Never loosen it and leave it, always make the final adjustment by tightening a bit. Even if you have to go too far and come back to what you need. Keep the screws under tension. I do the same for pickup screws. I don't want anything to vibrate...
Hmmm...I wonder what this button does...
Sometimes the crews pop up & out of the slots, check they are well seated.
Are your strings new?
Moving on.....
Quote by KenG
Sometimes the crews pop up & out of the slots, check they are well seated.
Are your strings new?

Yes, the strings are new, but it also happened with the old strings. Only now the buzz is much brighter.