I got into the show more or less by accident, and because my nature of not wanting to give up on something right away once I've start it, I ended up watching the entire 1st season.
I know plenty have done so already, but I have to compare it to Lost because of one reason, and it's not the time jumping aspect of it: Lost had me hooked from the opening scene all the way through the first 3 seasons. Right away, from that first stare of Jack's eye, his run through the jungle, the mayhem on the beach, I knew it would be an interesting show to watch. With Alcatraz I never got to a point of really caring what will happen. I never got invested in any of the characters. Another review here said that the show would have been much better had it stayed in the 60's all the time, and I have to agree. The scenes from that era are all great. You're immediately questioning the wardens motives along with his lackeys, and the back stories of the criminals promised much more potential than any of the stories for the present day people. And did I mention the warden? Must say, I think Jonny Coyne does an awesome job with his character.
In the present day parts of the show, everything is much more cliché. You have the tough female lead, the not so tough but brilliant side kick, a shady boss, the good mentor with a gray story of his own... And then you have the crime of the week which you can be 100% certain will get solved, already simply because the episode names suggest who's turn it is to be processed. Basically, it all plays out like any other crime drama on TV at that point, except you already know who the bad guy is. I don't think it's the fault of the actors really that the show doesn't take off. They're just not given an interesting back story to develop from. Let's be honest, the good cop trying to understand her past and having to chase the black sheep of the family in order to do so is not exactly ground breaking story telling.
Also, like another review stated, it is somewhat weird how little interest the task force shows in trying to figure out "how and why" the bad guys keep popping up from the past, instead they're always focusing just on catching them and putting them back in their cage. That doesn't feel like a good game plan. It's like always just putting a bucket on the floor when it rains instead of trying to fix the leak in the roof.
The somewhat strong rating of the show here on IMDb would suggest that it could get a second season, and the last episode does leave enough of the plot unsolved for it to be possible. But I doubt I'll be tuning in for another go at this one.