When picking up sts, always pick up from the right side. This will put the seam on the wrong side of your work (inside of mittens).
After picking up sts, when you work the actual row for the first time, check to make sure the sts aren't twisted. When you get to a twisted st, just slide it off your left needle, untwist it and slide it back onto your left needle before working it. These twisted sts happen if you wrapped the yarn backwards when you made the pick up st.
If you find yourself having to purl rather than knit, then you are on the wrong side of your work. i.e. you are working on the inside of the round rather than on the outside of the round. Either turn the round inside out to get on the right side (not always possible/practical), or turn the work (like you were doing a short row) and continue on the outside of your round.