Ignoring the pro/con debate to challenges, if you've actually completed one and it's subsequently archived, I currently cannot see a way to read your old log or view the picture, which is a shame as it's part of your activity.
I've set up a feedback vote but can't link to it here as I've not posted enough to be considered spam-free
Search for view archive challeng logs and it should come up.
May be worth voting on if you agree.
Link to post