Closures are basically global variables and inherit all of the problems with global variables.
Continuations are basically goto's or memcpy and inherit all of the problems with goto's and memcpy.
Functional programming is ALL of the bad programming practices of the '80s. But because it's more abstract and mathematical it gets a free pass. Nevermind the fact that computer science is not mathematics. And the benefits of mathematical abstraction DO NOT TRANSFER if they inherently violate the commandments of bad ideas like global variables and goto's.
There are solutions to ALL OF the object oriented problems--including the diamond problem, circle-ellipse problem, and overuse of type hierarchies. There are no solutions to the functional programming problems because they inherently incorporate bad ideas described in paragraphs 1, 2, & 3.