Use the same table and have a flag field for residence R, work W, vacation V,
etc.

I suggest that you simply create two sets of fields on the one table.

I don't believe this: there will also be the agent's address, the home
address, the one to send bulk material to, the billing address, etc etc.

Ditto: what about the opponent's knocking site, the unofficial fan site,
the IMDB page, etc, etc?

It's simply two straightforward one-to-many relationships e.g.

 People (
   PersonID primary key,
   FirstName,
   LastName,
   NickName,
   CurrentCredibility,
   etc )

 Addresses (
   BelongsTo foreign key references People,
   TypeOfAddress
   Street,
   City,
   etc
   Primary Key (BelongsTo, TypeOfAddress)
   )

 Websites (
   URL primary key,
   BelongsTo foreign key references People,
   LastVisitDate,
   etc
   Primary Key (URL, TypeOfWebsite)
   )

To make the compound primary keys, in the Table Design grid, ctrl+click
both fields and then click the yellow key Primary Key tool.

If the PersonID is an autonumber, then the two BelongsTo keys must be
long integers. Use the relationships window to drag BelongsTo over the
People.PersonID and remember to check ON the box for Enforce Relational
Integrity.

You might want to use another table(s) to control the contents of the
TypeOf fields

No: that way disaster lies. It will be one week after release when
someone wants a third address type, and then you'll be redesigning every
single table, query, form and report. Better just to design it right
first time and then sit back relaxing...

Hope that helps

Tim F