I watched the entire 8-part limited series on the History Channel. While I was slightly disappointed with the outcome (DNA testing of the shawl), I found all of the circumstantial evidence quite compelling. I can see how someone could easily believe that H.H. Holmes was indeed the Ripper.
The most compelling evidence presented during the limited series was the side-by-side photos of H.H. Holmes and the Ripper sketch, which was etched from all of the eyewitness accounts of the day. The sketch was pretty spot on. At that point it was hard to deny the possibility that H.H. Holmes could've been the Ripper.
As an avid Ripper fan (I've always been fascinated with the mystery of the Ripper), I've seen many documentaries surrounding the great debate of who he was. The circumstantial evidence surround H.H. Holmes as the Ripper tends to be the most compelling to date in terms of Ripper suspects.
Just because the DNA tests didn't deliver the results Mudgett had hoped for, it doesn't necessarily mean Holmes wasn't the Ripper.