No no no! You're not doing anything wrong! Your project looks great!
I would suggest working one round of single crochet around the whole thing before working any kind of decorative border. This will give you a uniform base to work in. Just work a single crochet into the end of each row. If it seems to buckle, then skip a row every third or fourth stitch and see if that helps to flatten it out. Make sure you work three single crochets into each corner on each round too!
My favorite border for a dishcloth or blanket or afghan is reverse single crochet, and I have a video showing how to do it HERE
. But if you want to try something else, you can find other border designs in THIS LIST
of crochet posts.
Hope this helps.