I made a Judy Martin Log Cabin quilt and I found that it is a must to accurately cut the logs and accurately sew the seams. I used a magnetic seam guide that i bought at joann's to keep my seams perfectly straight. It's too easy to veer off the bottom, throwing off the finished product.
I also pinned the bottom of the log if it was a longer piece - even 5 or 6 inches to keep the pieces even. Also double check you bottom piece when sewing to make sure that you edges are lined up even.
With log cabin pieces being narrow to start w/, sewing just a bit off really shows up.