the dark knight rises - When was Blackgate prison built?

Blackgate has always been in the comic but Batman's main foes aren't mainly criminals, but criminally insane. The criminally insane go to Arkham Asylum, the criminally guilty go to Blackgate. Blackgate is a prison; not a county jail, so Gordon isn't talking about Lau being held there. However, it is likely where Rachel was hoping Falcone would end up in "Begins", instead Scarecrow drives him insane and he's sent to Arkham instead. Rachel also mentions that Joe Chill and Falcone did time together, this (as long as it is in Gotham) would have to be in Prison as neither were declared insane at the time. So, by implication, they served time together in Blackgate.

As I said, Blackgate is in the comics, you can find it in No Man's Land(upon which much of TDKR is based), and I believe Moroni, the Falcones, and some of their hitmen are sent there in The Long Halloween (upon which much of TDK is based).
The introduction of this facility is just an expansion of the adaptation, much like more X men appearing in each sequel who weren't mentioned in prior installments.

Also, Blackgate is important to the plot of Rises in that it is a stark contrast to Arkham. Blackgate is meant for the imprisonment of criminals, versus the treatment of the ill as in Arkham. This is important to enforce the Dent Act's patching of the holes in the Gotham Justice System as evidently displayed in Batman Begins.