When the mistake is close to the edge, I would drop the furthest stitch from the selvage and unravel it down to where it can be fixed. I use then a crochet hook of about the same diameter as the knitting needle, then work the stitch up from the bottom, using knits and purls as appropriate. Then do the next stitch towards the selvage, and so on.
If you were working the stitches instead of slipping the first stitch, then you can leave the selvage stitch alone. It will go into a seam, but, if you think it shows, you can work that down the same as the other stitches. But it is more fiddly than the rest.
There are also double-ended crochet hooks which can be used to work up a variety of knit or purl stitches. Then you don’t have to pull the crochet hook out to change from knit to purl, you just pull this clever tool through. I have a set of four from Clover but really the ends are carved too sharply to do it with them, they are more double-ended Tunisian hooks which are shorter. The better tool is made of metal and the hook end is more rounded. I’ve seen them online but never at Joann, my local store.