I can discount the grandfather thing in Alcatraz. I don't believe they've provided enough information for us to say it's a big hole. Sometimes I have the same critiques about plot as you've mentioned and then the show turns to effectively fill the gaps. I have a feeling that's going to happen here, especially since it's getting obvious the grandfather character is going to play a much bigger role as the episodes progress.
There's a difference between leaving things unexplained and creating a glaring logic problem. If the rest of the show had been better I would have been willing to give them the benefit of the doubt. Instead, with the information we're given, we're strongly led to believe that she didn't know her grandfather was an inmate instead of a guard, and even worse she didn't know what the hell he looked like. When you have a character who is supposed to be very proud of her heritage AND supposedly a prodigious detective, that's too big a pill to swallow, even temporarily while we wait for an explanation.
I can also discount some of the wooden and cliché dialog in Person of Interest, because otherwise the show is rather good.
Do you mean "overlook?" That changes the meaning of your Alcatraz response in the previous paragraph...