I took my yeast slurry out of the fridge to warm it up to room temp before brewing. I had some technical issues however so I'm brewing tomorrow instead. At that point the yeast will be out of the fridge ( at room temp - aprox 20C ) for about 24-28 hours. It's in a mason jar and the lid is slightly loosened. Will it be OK to use or should I dump it and use a different jar?
The main thing to check for is actual yeast activity. The time it was left in or out of the fridge is a secondary issue. An active yeast culture with sufficient nutrients is actually quite stable. If re-supplied with nutrients it can be safely kept going (and be used for brewing) for years in "normal kitchen conditions"(ie not a fridge).
Yeast taken out of a fridge needs some time to return from being dormant (or being of very low metabolic activity) and 24 hours at "room temperature"(20C) should be enough. If the yeast culture is active and has nutrients/sugars then it will ferment. Fermentation can be judged by the amount of bubbling and foam on the surface of the yeast "solution". If the yeast is actively fermenting then it can be pitched into a brew. If the yeast is not active then wait until it is or make a new culture using new yeast - AND MAKE SURE THAT IS ACTIVE TOO.
If yeast (liquid or powder) is added to a weak sugar solution and kept at room temperature for a day it should start actively fermenting. A good active yeast will start fermenting withing minutes and bubbles and foam might be seen on the surface of the solution within 30 minutes. If a correctly made up yeast starter culture does not show signs of life within a day (and I would say within 4 hours) at 20C then IMHO it should be discarded with any yeast source it was made up from.
It should be fine to use. I'd decant the spent liquid from the jar and add some fresh wort and let that sit until I had signs of yeast activity in the jar. If the new wort has to sit in the fermentor until the yeast have awoken so be it. If your sanitation is good that should be a problem for the wort to sit for several hours. I regularly pitch the next day some of my beers. Again your sanitation has to be spot on.
If the jar doesn't start, that's when I'd look at using a different jar. But I'd try restarting that one too with some starter wort.