Yes. BUT... Admitting mistakes by itself, gone too far, will fail. BE open and candid--it makes you approachable, it teaches and develops others in the processes of leadership and management. But you need another ingredient too: you must reduce the anxiety of the organization at all times, not increase it. This is the secret, hidden ingredient of real leadership that's easy to overlook. (See this awesome YouTube video about it: www.youtube.com/watch?v=RgdcljNV-Ew)

So, like you say, let them see you sweat, BUT never in a way that leaves them feeling real fear or doubt about the outcome. Raise the problems, let them tackle issues with you, but make sure they know that an awesome solution is always in sight.