It's good to have a take-along project. Something to be useful during otherwise wasted time, like waiting rooms, or riding the bus. Mine, when I remember to bring it along, is an edging from one of Tina Frauberger's books, wide enough to look impressive, but works up faster than you would expect. (You can find her books on Georgia's Online Archive of Tatting Books in the Public Domain, click here.
Of course, at the end of the bus ride, I found a mistake in the very first thing I did that day. 3 rings and a bunch of chains later, unpicking so many stitches would frazzle both the thread and my nerves beyond breaking. To avoid more loose ends than I wanted to work in, I used my old pull out the core thread trick. I unwound both the shuttles. Then working back bit by bit, I would pull up a loop of the core thread and pull it all the way out. As you do this, the end of the thread will want to flail about, so I hold it between my legs and gradually pull it through to reduce the twisting and tangling.
Sticking a crochet hook into a picot and then pulling on the core instead of the picot is a good way to get a grip on the core thread. That's a common way to open up a ring, but I'm doing the same thing with this chain. Once you have worked all the way back to the mistake, then you can put the thread back on the shuttles and begin again. Does this fix take more time than cutting the threads? Yes, but no ends to work in.