You can fix the runs with a crochet hook, but with garter, you'll have to work one stitch from the front and one from the back, since you essentially have a knit row and a purl row as the work faces you. Sometimes it's easiest to flip the work over rather than to work from the back. The video shows stockinette stitch, though.
As you fix the stitches, you'll be able to see if they're right or not.
Temporarily secure all the stitches with a stitch holder or strand of yarn and work one at a time with the crochet hook. When you get to the edge, sew the loops to the edge with some yarn to secure them.
If it's any consolation, as soon as I think a project is going great and error free, the fates make sure I don't get to sure of myself. :rollseyes: