OK, but wrong...

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So a quick question for my mathy friends.  I often hear from students these words. 

"I got it wrong, but I know how to do the problem." 

The student has mastered the procedure or understands what is being asked, but makes a mistake or several in the process and the result is an incorrect answer.

This is very common in my advanced classes where students are asked to understand and solve complex, multistep questions.  They often know the solution in theory, but cannot execute the later, simpler algebra or arithmetic of the problem accurately.  My response is to circle the error and write, "OK, but wrong."

As we think about the teaching, learning, and using of mathematics, is it enough to know how to do the problem, even if you can't get the right answer?

Where is the line between understanding in principle and correct solutions? What do you think?