For both diamond dishcloths, we started out rows with ch 2 followed by a dc into the last dc of the previous round -- instead of making a ch 3 as a replacement for the first dc of the row.
The main reason for this is to give a nicer edge for times when you don't want to crochet on an edging later. The reason that this gives a nicer edge is that crochet stitches don't rest exactly on top of each other.
In knitting (in plain stockinette), each knit stitch rests squarely on top of the stitch from the previous row. (A notable exception is when one knits through the back loop across every other row. But, we're not going to go into that here.)
In crocheting, this is not the case. The stitch rest just a little bit to the right of the stitch from the previous round. This can be most clearly seen in the picture in the second row from the top (a right side row). The dishcloth ended up square because when working on the opposite side of the dishcloth, the new stitches will also rest a bit to the right. And that "bit to the right" looks like a "bit to the left" when looked at from the first side. This can be seen most clearly in the first row from the top (a wrong side row from this perspective).
The ch 2 at the beginning of a row fills in the side a little. By the way, if we started the row with a ch 3 substitute for a dc, there would be a small gap between the ch 3 and the following dc.