CactiGuide.com

I moved my plants to a brighter but colder (and sometimes drafty) part of the house and for some of them their dirt is taking awhile to dry now. I'm worried about rot. In general, how long is too long (at temps in the 60s)?

This is tough to give an exact answer!
The general rule is that your compost should be free draining so it doesn't stay wet for long. There is a big difference in rot risk between wet (especially waterlogged) and damp compost, and it depends a lot on your species too.

If you are using a free draining compost and surplus water is not collected beneath the pots there may not be an issue.
60s F (>15deg C) is not cold. Many species which don't need heat will be happy in these temperatures, and will even be growing, so having it as bright as possible is good. Many Crassulaceae, Mesembs and higher altitude or more temperate latitude cacti (Cleistocactus straussii or Orecocereus seem to grow for me in the spring and autumn when it is cool) wont be too fussed by a bit of damp.
On the other hand, if you have a load of Ariocarpus etc you may be headed for trouble, and may need to reduce or completely stop watering (perhaps not until April or even May).

It's very useful if you say where you are living too. Northern or Southern hemisphere, for example?

It's soil. Dirt is very different matter
As stated earlier, it depends on the plant and if it's growing or not. You can't assume the same for all plants. My aeoniums, sempervivum and rosularia are outside under rain with temps between 8 and 17. It's their growing time so they will take the water. Even a jade plant is growing slowly. But if i were to water my cacti in these conditions, rot is inevitable.
Tell us about your sun exposure, temperatures, type of pots, what plants...

The plants are healthy, growing young plants grown from leaves or small cuttings (except one that rotted, but it was already having issues). It's winter here, they're getting ~9 hours of bright but often cloudy light in a south facing window. The soil they're growing in is 50/50 potting soil/small gravel mix in a plastic 9 cell pot

Mysteriously, other the same soil in other similar pots has had no issue drying. I watered everything on I think Monday, and the other pots' soil has dried to just slightly damp, while the one I'm worried about is still saturated. It's less than a foot away from most of my other plants. If I didn't know better, I'd think somebody's been watering it.

Am I right to be worried about rot at this point? The soil has even started to mold. Is there a way I can safely dry it out?

I took another look at my pot that won't dry and it looks like the bottoms of the cells are crushed upward, creating a space for water to pool. I'm about to take the plant and dirt out and put them on a tray to dry, then try to fix the pot or get another one and hopefully I won't have that problem in the furure

But more generally, I am curious about what length of wetness and dryness plants that are growing need. Unfortunately, I don't have an ID for most of my plants, they were grown from unlabeled leaves and cuttings I was given. I do know I have eschervia, sedum, graptosedum, and crassula

It depends on the temperature. The hotter the atmostphere is, the longer the plant can tolerate wetness (up to a point and dependant on the species). However total dryness is necessary between waterings (excluding seedlings and small very young plants)

The lenght of wetness depends on the species you have I believe. And the soil and the material of pots and and size of pots and the humidity of air. In general the soil must be completely dry before watering again, smaller pots tend to dry faster than bigger ones. Some need watering once a month, some once a week or so. If there is high humidity in air the soil dries slower than when the air is dry.
There's a difference between a wet soil and moist soil. The soil shouldn't stay wet. Properly draining soil stays moistened but not that much it rots the plant.
I can be wrong since im just a beginner but this is as much i've learned by reading

I dug everything up to put it in a pot that wasn't damaged, and the roots all looked very healthy (they looked feathery), not at all suffering from being in soaking wet soil for 5 days. Which was quite a relief

Thanks for all the replies