If your u2addr-table isn't extraordinary large, you could just fetch the whole thing in a hashref and loop through that:

my @results;
my $hr_addresses = $dbh->selectall_hashref("SELECT addr, id FROM u2add
+r", "addr");
if (!defined $hr_addresses) { die("Error executing query: " . $dbh->er
+rstr); }
foreach my $addr (@addr) {
    if (defined $hr_addresses->{$addr}) {
        push(@results, $hr_addresses->{$addr})
    } else {
        print("Error, ID of address [$addr] not found\n");
    }
}
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The use of selectall_hashref (or selectall_arrayref) relieves you of having to prepare, execute and fetch* everything yourself. All that's left is to use the results (in this case as an in-memory hashed lookup for all addresses in @addr). On top of that, calling finish isn't neccesary when you are fetching *all* the results, only when you want to abort fetching results partly through.
Besides that, if selectall_hashref (or selectall_arrayref) returns undef, then executing the query went wrong. This is a very nice thing to know. This is also different from the query executing correctly, but returning no results (which is slightly more difficult to check when using fetchrow_array).

Edit: Whoops, got the keyfield of the query wrong, fixed now.