Using Grand Central Dispatch to fetch data from Parse.com and update UI asynchronously
First off, I don't know Swift.  These are generic issues that should be addressed in all written code, and I'll leave the Swift-specific stuff to the experts.

Comments


//execute slow task



Comments should say why the code is the way it is, not a generic comment that doesn't tell us anything constructive.  If there is an issue with the code being slow, document why it is slow, and maybe state why you haven't been able to fix it for future reference.

Spacing


    }




}



We definitely don't need that much whitespace hogging our screens.  It forces code off the screen, it increases scrolling, and generally slows us down when reading and understanding the code.

Indentation


} else {

    if let errorMessage = error?.userInfo?["error"] as? String {
        self.showErrorView(error!)
        }
    }



Your indentation is off there.  Each closing brace should have the same level indentation as the opening brace, unless they are on the same line, which is rare.

Naming

Your names should state what the function does or variable is, and only what the function does or variable is, and the variable/function shouldn't be/do anything but what the name says it is/does.

done() tells me nothing about what the function does.

qos doesn't tell me what the variable does, what it contains, or what it is used for.

self.loadObjects() appears to do UI updates, according to the comment.  Loading an object is not the same as displaying it, and loading and displaying from a single method violates the Single Responsibility Principle.