My general issue with these things has always been that I think organisaitons ought to play to their employees' strengths, rather than focussing on weaknesses (since there is no universal concept of weakness (outside of criminal and anti-social behaviour), only suitability to the job you're paid to do).
However, having been through a lengthy psyochmetric testing exercise last year in work, I now have a good idea of what my "strengths" and "weaknesses" are (or my suitability for my role and others within the business).
To answer the question:
Admitting or showing signs of weakness or vulnerability.
Admit when I can't do something, or if I need help.
As a lawyer, this isn't usually seen as a weakness (admitting you don;t know something is the weakness). But for so many other jobs, saying "I don't know" and "Can you help me with this?" are pretty valuable tools.
But it took a psychologist to get me to believe this....