Bob,
This is all fairly old business. A certificate provides assurance to
others that the public key in the certificate is assigned to the
person named in the certificate. If the certificate is issued within
the Internet certificate hierarchy, then the corresponding PCA has
filed a publicly available statement indicating the degree of care
each CA and user under it is expected to exercise in ascertaining the
identity of subjects named in certificates and the degree of care
issuers and users are expected to exercise in protecting private keys.
Nothing more is implied. There's no information in the certificate
about any rights, privileges, authority, etc. associated with the
named person.
The liability associated with signing something is presumably related
to what the document is and who signs it. Presumably, the liability
is neither greater nor less than for a wet signature on the same
document.
Steve