I have clay pots with some tough dirt or mold that hot water and scrubbing just won't remove. I need something safe to clean the pots with, they are for cacti.

I make up a solution of 1 part bleach to 5 parts water. Since I want enough to cover whatever size clay pots I want to clean/disinfect, I might make up 2-4 gal. of the solution in a bucket. If its 3 gal., that would be 2 qts. bleach and 10 qts. water. I use hot water. I just put the pots in the bucket and pour the solution over them, enough solution to cover the pots. I let them soak for 30 minutes but longer won't hurt a thing. Then I take them out, and while they are still wet with the bleach solution, I scub them with a 3M scrub pad, those green pads found in grocery stores. Then I will rinse them off and put them somewhere to dry.

Be careful with the bleach solution. You might want to wear water-proof gloves and don't get the solution on your clothing.

I do basically the same as @drdawg suggests, but I let the pots soak overnight, or even for a day or two. I keep a plastic bin outside for this purpose because I'm allergic to bleach fumes. Then after scrubbing them with a 3M pad I let the pots soak in clean water for a day, then let them air dry on a hot, sunny day.
Here is an image of the some I got from a Free-Cycle...they were seriously in need of cleaning, but look how beautiful they are now!

My understanding is that it is better to wash/scrub pots in soapy water first, then dunk in bleach solution because the bleach can be de-activated by organic matter if any remains on the pots.

That's not a bad idea but with so much solution, I doubt that what little organic matter would be present, would diminish the bleach activity whatsoever. I don't know this and I do in fact pre-scrub my pots before putting them into the bleach solution. I just want to remove as much grim as possible so that the bleach solution works more quickly and more efficiently. I just rinse the pots in clear water after the bleach soak/scrub. I actually like having a tiny bit of residual bleach in the porous clay to at least temporarily prevent mold returning.

I kind of assumed that a person would have already washed the pots before disinfecting....that's what I do. Sorry I didn't spell it out in my post.

I am reminded of my grandmother washing her laundry. She would first wash the clothes, then rinse, then put them in a bleach solution to disinfect them...then one more rinse. Lots of water, but the clothes (and the clay pots) are clean and disinfected.

All these suggestions are great if your aim is to disinfect. That wasn't made clear in the original question.
Or, is the aim to clean and make them look good?

Most clay pots become embedded with (white) calcium deposits that build up as moisture continually evaporates from their surface. Your scrubbing will remove what you can physically get to, with or without the bleach. From a chemical point of view, bleach (which is alkaline) will not remove calcium deposits (also alkaline). Calcium embedded in the pores of clay can be dissolved with a mild acid. I'm not sure what a good mix would be, but given that tap water is already seriously alkaline, I would start with white vinegar (pH 3-3.5) mixed with water at a 1:5 ratio for immediate scrubbing, or 1:30 for an overnight soak - see how that works, and make adjustments if needed. Greene's suggestion to post soak in clean water applies to both basic (bleach) and acid soaking.

A solution of CLR would work quite well.

I can't remember where now, but I read once that it is better to not disinfect or do anything but rinse off clay pots. Something about the pots being more organically healthy for plant growth if they were left alone. It was supposedly especially true for using them as containers for sprouting seeds. I remember it because I basically ignore mine and don't bother with any kind of cleaning. I just reuse them as they are. At most I've only worked on the outside of some just to see if I could make them look better. Normally I don't bother. I've never had anything negative occur from reusing a clay pot without it being cleaned. Obviously, I avoid labor when I can .

Be careful with any of the acid cleaners (calcium-lime-rust removers), although CLR is likely one of the least caustic of them. These are stronger acids usually with a pH of 2 or even pH 1 (or less). The pH scale is logarithmic, meaning pH 2 is ten times more acidic than pH 3, and pH 1 is ten times more acidic than pH 2 (or a hundred times more than pH 3). Just diluting them more doesn't do the same thing. While they would dissolve the calcium deposits well, I just don't know what might happen to the integrity of the pots themselves in the long run. You would never be able to remove every bit of it in such a porous material as baked clay, even after soaking in clean water.

Like Donald, I don't disinfect my pots, either. I don't even worry about seeding soil being pasteurized (and certainly never sterilized). I rely on the balance of mother nature's organism living together, that usually keeps things in check. On the other hand, if you are drastically changing the overall natural environment, like in a greenhouse (for instance), then one might need to take such measures.

We use vinegar here to remove mineral deposits from items due to our hard water, so I would have thought it would work although I've never bothered removing them from clay pots. But I just want to add, in an abundance of caution because probably nobody here would do it but it has been done, do not try and do the vinegar or other acid and a bleach soak at the same time because combining bleach with an acid produces toxic gases.

Every now and then, one or more of my clay pots will get covered with white, powdery mold and something like bleach is the only (simple) thing that will get rid of it. If I just clean it with soap and water, the mold always returns quite quickly.

Compared to stuff like muriatic acid, CLR usage is a piece of cake. You just have to determine what dilution works. You would want to use the weakest solution possible.

You are so right Sue. Never mix bleach with anything else, other than plain water. If you do so, you will be in for a nasty result. Ask me how I know.

sooby said:We use vinegar here to remove mineral deposits from items due to our hard water, so I would have thought it would work although I've never bothered removing them from clay pots. But I just want to add, in an abundance of caution because probably nobody here would do it but it has been done, do not try and do the vinegar or other acid and a bleach soak at the same time because combining bleach with an acid produces toxic gases.

I think that's a very good reminder, Sue!

Also -- although presumably one would be wearing older clothes while doing gardening stuff -- keep in mind that bleach can really do a number on fabric !

Just a sidebar - Once soaked, cleaned, dried and set aside till use, it's a good idea to re-soak clay pots in plain water just before use. Clay pots used later w/o a just previous soak may hamper initial plant adjustment because an unsoaked clay pot may absorb that first plant watering enough to interfere w/ said plant's compatibility in it's new clay pot home.

I think it's always better to soak a clay pot before planting, whether it's new or used, washed or unwashed. I don't always do it, but I do much of the time.

I'm with you Donald, both on soaking and on the casual attitude towards disinfecting. Here in FL where we have every bug and fungus there is, I figure as soon as the plant gets outside again, and especially if it is going to sit on the ground it's infected again anyway. I hose my pots off, scrub them if they have algae growing on the outsides (which happens a lot here) just for appearances, and carry on planting.

Only for orchids do I take any precautions, - a scrub/soak with Clorox Cleanup, soap and bleach combo - as the plants are especially susceptible to fungal infection. But again, my orchids grow outdoors, so there's no preventing fungal infection without major fungicide preventative spraying anyway.

I wish I had taken pictures of a couple of the 8" clay pots where I have bromeliads growing. If you knew what that clay-covered white, powdery mold looked like (and felt like), I can assure you, you would have headed for the bleach. They were really gross and it seems that the mold appeared within just a few days. I divided some older bromeliads and potted up these divisions in new clay pots. These pots were in the solarium. I have never seen my clay pots get "attacked" by mold like this in my greenhouses. I have a feeling that better air-movement and perhaps the higher heat in the greenhouses were the differences.