How does one "authenticate" a bitcoin user? What is the minimum standard for authenticating a bitcoin user. Would it be enough, for instance to verify that someone named "Tom Au" will answer to that name at this email address? Or are more detailed checks required?

Edit: Authentication would mean that I am what I say I am, that I am a human being and not a robot,and that I can do what I purport to be doing (trading Bitcoin).

Is there a public, or central registry for computer users?

In this event, would something as strong as "hashing" be needed for data storage and retrieval?

Would a web of trust concept work for the bitcoin community?
There are different KYC (Know Your Customer) laws in different jurisdictions, but generally it takes information that is difficult or very time consuming to falsify. License/ID scans, utility bills, and SSNs are examples

Suggesting "hashing" as a KYC solution suggests you do not know what hashing is (unless you were referring to the way a server should store such confidential information). I suggest you use the search function or explore bitcoin wikipedia to learn more.