What are some of the criticisms leveled against exposing continuations as first class objects?
I feel that it is good to have first class continuations. It allow complete control over the execution flow of instructions. Advanced programmers can develop intuitive solutions to certain kind of problems. For instance, continuations are used to manage state on web servers. A language implementation can provide useful abstractions on top of continuations. For example, green threads.
Despite all these, are there strong arguments against first class continuations?
First up, there is more then just call/cc when it comes to continuation. I suggest starting with Mark Feelys paper: A better API for first class continuations
Next up I suggest reading about the control operators shift and reset, which is a different way of representing contunations.