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I just found out that the filter for a tank with turtles in it should be at least for tanks 2 to 3 times the tank's size due to the fact that turtles are messier than fish. Does that rule apply to filters that are designed for turtles too? I have one of those Zoomed filters made for tanks around the size of 10-35 gallons. I have a 20 gallon tank. Do I have to triple the capacity of the filter (get a new one perhaps).

I've never heard any good things about "turtle" filters. Those seem to be made for those special "turtle" tanks which aren't recommended for an RES. It's more the gph that you want to look into not so much the size that it's rated for. I know that my Aquaclear 110 is rated 500gph.. and there are others that are rated for larger tanks that don't filter as much. There is a whole discussion on the filter "rules" some where in the forum.

I'd go with a fish filter next time.
Check the gph. Look for one that does about 10x the tank size.

The filter that I currently have is 3 1/2" by 3 1/4" by 1 1/4" at its widest. Its gph is between 30 to 55. So I might guess it is pretty mighty for its size.
I've refrained from fish filters because I had a bad expeience with one myself. One of my turtles almost got cut becaue it got its paw stuck in the intake tube of the filter. Plus it was spilling water all over the place because the tank is only half full with water.

The gph is 30 to 55?? That's not nearly strong enough to filter a turtle tank in my opinion. As for the problem with the intake of the filters you can remedy that by covering it with a piece of old stocking (clean of course) or a piece of sponge (make sure it's not been chemically treated). That can also act as a pre-filter and pick up some of the bigger pieces of garbage in the tank. I gave up on the sponge because it slowed down the filter's intake.

sounds like you have that cruddy zoo-med turtle 501 filter thing. Those things suck, get a better one soon

Yes, those Zoo-Med 501 filters don't have a good reputation, and the GPH rating you gave really is inadequate. The better the filter, the better the water quality.

I just remembered my tank came included with the filter and the parts. I took it out because of the problems with it (I also had a problem with the cascade the filter created in the tank), and replaced it with the Zoomed thing. Should I reuse it and take the Zoomed filter out? Of course, it's been a little dilapitated over the months.
Oh yeah, before I forget, can a piece of screening be a good thing to cover the intake with. Is it dangerous to turtles?
Also, I might upgrade to a 55 gallon tank soon. Any ideas on the filter I should buy?

Why has the first filter become "dilapitated" over the months if it wasn't being used? More filtration is better, but you said that you weren't satisfied with the first filter?

I wouldn't use metal screening in case it rusts.

Upgrading to a 55 gallon would be good. I'd get a Filstar XP3 for it (a canister); you'll be able to still use it when you go with an even bigger tank/container.

What about plastic screening?

What would be a good thing to muffle up the water noise in case this XP3 filter makes the water cascade out of it? I absolutely went nuts with the first filter because I couldn't sleep.

Actually, the gph of the 501 is 79... which still only makes it good enough for an 8 gallon.
Fill your tank up more, your filter will make less noise.
The XP3 is a canister filter, not a waterfill filter.

Filling up the tank won't work. For one thing it'll drown out the basking area. And I don't have much confidence in the Zoomed docks since my turtles aren't accustomed to a land mass floating over them. Also, one of my turtles is a full blown escape artist. It can climb up almost any surface, and given the plastic ledge than holds up the hood of the tank, escape would be as easy as 1-2-3.