These photos show how the hat patterns look before working in the ends on both the inside and the outside of the hat. When you knit circularly your patterns do NOT line up at the end of the row. Think of the stripes on a barber pole or a candy cane - they're actually spirals. If you look at the photo, especially the stripes, you can see the spot where the stripes don't meet. This is called the color jog and is the bane of many a knitter.
There are several techniques used to assist knitters avoid the awful jog. The best article I've seen on the subject is called "The Jogless Jog" by Meg Swansen in the winter 1996 issue of Knitter's Magazine. She details four techniques for four different circumstances: unconnected motifs, speckles, connected motifs, alternate color stripes, and solid stripes of two or more rounds. Vogue Knitting also did a short article on the subject in their winter issue a few years ago.
It really does vary on the specific pattern and on how successful the end result looks. There is no one perfect solution and some can be quite complicated, involving moving the end of the row over each row. If you're doing a complicated, not-easily-memorized chart, this particular jogless jog technique can drive you over the edge. I personally do not believe there is a perfect solution and I think most of the solutions are visible.
Judy Gibson has her own take on this situation HERE. She first shows you what one of the Meg Swansen jogless jog technique looks like and then shows you her own method of dealing with it. My method has one thing in common with Judy's. It involves breaking the yarns as much as possible. Yes, I know there are more ends to weave in which can be time-consuming. Even if there was no problem with jogs, I think carrying unused yarns upward too many rows can cause holes or lumps or tension problems.
For my method you simply cut the yarn when you are done with a particular color. Then look at the back of the work in the photo above. You'll see for each color of yarn you have a yarn tail coming from the right side and one coming from the left. Take the tail coming from the right side and work it in down over on the left side in the same color stitches. You're taking the yarn tail, crossing it over and working it diagonally to make the stripe line up. For the tail coming from the left side, work it
up over on the right side in the same color stitches. Here are photos of the inside and outside of the hat after the ends are worked in using this method. I've used the reverse stockinette stitch method of weaving in the yarn ends (I've discussed this here before) which is pretty invisible on the inside of a garment.
As you can see you can still tell where the jog is if you look at the 2-row stripes but it isn't terribly noticeable overall. Sometimes you can alter the pattern design a bit to avoid the jog by adding a one-stitch column of the background color between the pattern. Or add a vertical column between patterns in the contrast color. Just one column of one or two stitches done in the same color can offset any color jog pretty well.
Another solution I use is to simply knit one or two edge stitches in the same color to make a vertical stripe as shown in underside of the Dale of Norway Ringblomst sleeve here. This method seems to look best if you use the darker color yarn for the edge stitches.
I'm taking a few days off to finish the booklet. I'll be back Monday.