I have been using some mineral turpentine to clean paintbrushes and it's gotten quite dirty (it also got all gel-like, I think there was something else in the container it reacted with). Since these solvents are pretty toxic, how do I dispose of it correctly?
Local regulations about how to dispose of small quantities of solvent vary widely, so expect that Answers may be only guides to how you might be able to do it where you live.
Don't throw it out if it's still usable
Contaminated spirits is still potentially useful as-is for certain 'dirty jobs' like degreasing and cleaning up of old tools, engine parts etc.
I keep a jar of dirty spirits for precisely this reason, carefully labelled so I don't accidentally try to clean a brush in it. It has a little Vaseline, liquid paraffin (mineral oil) and various unknown lubricants dissolved in it from rinsing and cleaning of new and old tool parts and as far as I can tell it works just as well as fresh, clean spirits.
Keeping it going
In addition to the above, dissolved contaminants will usually settle out of solution over time. Let dirty spirits sit in a jar for a while (a few days to a week or more) and see if the stuff will separate to a discrete layer on the bottom. It usually will, then you can decant the 'clean' spirits off the top.
If anyone reading needs to do this on a larger scale see the pic posted at bottom.
In theory spirits can be kept going indefinitely this way. If you never top up there will come a point when it becomes too dirty to continue to use (it will be in effect very dilute varnish) but even then, simply decanting to a fresh container and diluting with fresh spirits can be all that's needed for the gunk to settle out. To be frank though the volume is so low at that point that few would mind the waste of throwing it out, or otherwise disposing of it — see next point.
If you use the settling method you're left with a small amount of sludge in the bottom of the container (it can literally be just a spoonful or two from a large jar used to rinse brushes all year) which can be disposed of safely in your regular rubbish collection. It is safe, but may or may not be legal depending on where you live and how OTT the safety regs are there (anyone living in California, we feel your pain) but it should be legal to do this everywhere because the residue can't be any more toxic than the original paint and/or varnish was. So as odd as it might seem residue like this is no more or less dangerous than any dirty paintbrushes or rollers, paper towels or wiping rags used in the painting or varnishing process, and of course most people wouldn't even think "toxic waste" when disposing of those.
If you still want to get rid of it but aren't sure how
This is going to horrify some people but a viable alternative approach for the typical small volumes of solvent we're talking about here is just to put it outside to evaporate (under cover as needed so pets etc. can't get to it).
This does sound environmentally very suspect but compared to industrial/commercial output of solvent vapours the amount of pollution this represents is irrelevant — even collectively for every leisure woodworker in the world, the amount would be insignificant on a global scale.
If you need to work through a large volume of contaminated spirits on a regular basis you might want to rig up something similar to the below to make the settling and decanting processes a little more efficient:
Highly volatile solvents like mineral spirits evaporate quite readily, so one option is to simply leave an open container outside and let it evaporate. The more surface area, the faster it will evaporate, so a large shallow pan is better than a tall and narrow container.
Once all the liquid has evaporated you should be able to dispose of the container in your household trash.
Many local municipalities have a drop off disposal site for hazardous chemicals. That is your best bet. If your city doesn't have such a service, here is a site that lists some other options.
What I've done is followed as above. Use it until it's at that point where it's useless. Then I've tipped it into land/sand/bushes etc. The land will filter it. Of course some substances, paint particles etc, left behind will have no negative effect on its surrounding. Maybe once they're dried up dispose of them. If tipped into a bin or sink, would have a much more severe consequence. I don't think there's a perfect way of disposal. The fact you're asking the question shows you're considerate of the planet. I know painters and decorators that give less of, ahem on a daily basis. Not reusing brushes, paint trays at all, which is a shame. I don't think burning sounds quite right. I would never burn melomine or painted products for instance. But I overthink a lot.