The side seams on some of the tees are actual seams using a serger, i.e, a straight stitch seam and then the serged edge or approx. 1/4". These are the ugly seams/knots I first mentioned. And when one stretches the "yarn" these seams curl to the outside, thus they show up when crocheting. So when selecting old tees, look for the ones that are made from "tube-like" fabric that have no seams.

To make the "yarn" continuous, one of the demos shows to lay the tee flat with the bottom hems aligned. Cut off the bottom hem and then fold the tee in half lengthwise less 1". When cutting using the rotary cutter, do not cut thru the 1". Cut across all the way up to the underarm. W/scissors cut at an angle between the rows to make a continuous strip.

I have since pulled out the rug I attempted to make, cut off the "uglies" and will try again.

Thank you all for your responses and links. You have been so helpful.