The RHSS is fine for practice, I even use it for making things. Generally it will show your stitches well so you can actually see the pattern. You are picking up stitches which will throw things off. Be sure you bring the yarn under the needle at the end of the row; it is easy to pick up a stitch at the beginning of the next row if the yarn is over the needle. Sometimes if a stitch is not worked completely and moved off the left needle it will look like you have another stitch to work on the next row. Inadvertent yarn overs are also a problem, be careful of how you move the yarn from front to back and back to front. http://www.knittinghelp.com/videos/knitting-tips
Click the link, scroll down and find the Seed Stitch aka Moss Stitch video. Amy shows how to move the yarn in the Continental video, I'm sure that's true for the English one as well.