Elsevier told me the following concerning implementation of addresses in Scopus: “For recent and ongoing records we include all author affiliations, if they were available in the original source title. However, we have not been able to source affiliation data for all archive material. In some cases only the first author address is included”.
Scopus is labelling author search field affiliations as seen on this screenshot:

When Scopus has implemented all address information,
contrary to Web of Sciecne, they connect each author
with the exact affiliation/address by using letters
alphabetically from a, b, c etc. Look at this screenshot:

As you see in the screenshot they also use two icons right behind
the last author.

The letter icon points to the corresponding e-mail address and
the pencil-on-paper icon links to the corresponding/reprint
author address and e-mail again.
If searching, like in the Web of Science, for authors Haglin, L and
Rantapaa Dahlqvist, S and then limited search for address umea you
get the following result as seen in the screenshot. Be aware that

Rantapaa Dahlqvist is searched both with single first name 
initial S and then both initials S B.

This means you loose 9 records from Rantapaa Dahlqvist, S(B) and 5

from Haglin, L. 3 of the

records from the search on Rantapaa Dahlqvist, S(B) are from 2002,
which does indicate that missing

addresses is not just a problem for older records.

This screenshot shows a sample record
from journal Rheumatology 2002 lacking addresses for

Rantapaa Dahlqvist, S(B).

Checking the original electronical article in the following screenshot
shows that address for Rantapaa Dahlqvist, S(B) and co-authors
at same institution are included.