User blog comment:J Fan/Idea about Barbossa in POTCO/@comment-75.89.162.74-20130109052810/@comment-1984959-20130109174519

Regarding CotBP, the writers stated that they hadn't decided on an approximate date, sticking to the idea that the films take place some time between 1720s and 1750s. The same obviously went for DMC and AWE. As for OST, well...they kinda intended to place it in the 1750s, including writer Terry Rossio, but someone kinda made it to where the film took place approximately at 1750, particularly from a "Pirate Execution" sign(look here).

As for Blackbeard, that's a bit simpler to explain. Just take out the idea that Blackbeard was really beheaded. Yes, it was mentioned by Jack, but I was able to find this statement from Terry Rossio:
 * "Blackbeard's history is definitely a legend, and like most legends, may or may not have a basis in fact.

So it's safe to say that Blackbeard's history is legend, including his own death. Best way to explain how he was still alive. Also consider the math - if Blackbeard hadn't died in 1718 and lived to the 1750s, he would be in his 60s(which was how old Ian McShane was).

Hope this helps clarifies things. :)