It's pretty common to have ladders with dpns especially when you start out. Practice seems to make them disappear. You can try tugging just a little on the yarn on the first stitch of the new needle to help close the gap. You can also move the break
between stitches by knitting the first stitch on the new needle onto the previous needle. If you do this all the way around and repeat it every couple of rows, it'll keep the ladder from forming in the same place every round. Some of the ladder will ease into the side sts as you wear the warmers or when you wash them.
Using the crochet hook to pick up the ladder will leave a hole. The ladder isn't a dropped stitch, it's the connection between sts so you're creating a stitch and leaving a hole that's really a yarn over at the bottom of the ladder. If you do it regularly though, it could be a design element that's all your own!