General synonyms:
* Imperfection
* Error-proneness
* Incapacity
* Liability to err
* Weakness
* Vulnerability
More specific synonyms:
* For human beings: frailty, human nature
* For systems: unreliability, deficiency
* For arguments: unsoundness, flaw, weakness
The best synonym for "fallibility" will depend on the specific context in which you are using the word.