Well, it's been seven hours since the OP was last seen here, so at this point I can take a crack at it for fun without feeling like I'm doing free work.

#!usr/bin/env perl

use strict;
use warnings;

sub is_street {return shift =~ m/^\d+/;}
sub is_postal {return shift =~ m/^\w+.+\d$/;}

sub street_components {
    my $address = shift;

    if ($address =~
        m/^
            (.+)
            \s+APT\s+                       # APT anchor
            (?:\(Range\s+)?                 # Range syntax
            ([\w\d]+(?:\s+-\s+[\w\d]+)?)    # Apartment number
            \)?                             # Closing range syntax
        $/x
    ) {
        return {street => $1, apartment => $2}
    }
    else {
        die "Street address match failure: <<$address>>\n";
    }
}

sub postal_component {return shift}

sub apartment_expand {
    my $apartment_range = shift;

    my ($low, $high) = split /\s*-\s*/, $apartment_range;

    return [$low] if !length($high);

    my ($low_num,  $low_alpha ) = $low  =~ m/^(\d+)(\w+)$/;
    my ($high_num, $high_alpha) = $high =~ m/^(\d+)(\w+)$/;

    my @return;
    foreach my $num ($low_num .. $high_num) {               # Numeric 
+increment.
        foreach my $letter ($low_alpha .. $high_alpha) {    # Alpha in
+crement.
            push @return, "${num}${letter}";
        }
    }

    return \@return;
}

my %record;
while (my $line = <DATA>) {
    chomp $line;
    next unless length $line;

    $record{'addr'}   = street_components($line) if is_street($line);
    $record{'postal'} = postal_component($line)  if is_postal($line);

    if (exists $record{'addr'} && exists $record{'postal'}) {

        my $apartments = apartment_expand($record{'addr'}->{'apartment
+'});

        foreach my $apartment (@$apartments) {

            printf "%s, APT %s, %s\n" =>
                $record{'addr'}->{'street'},
                $apartment,
                $record{'postal'};
        }
        undef %record;
    }
}

__DATA__
432 10TH ST APT (Range 2A - 2B)

BROOKLYN NY 10598-6601

432 10TH ST APT (Range 3A - 3B)

BROOKLYN NY 10598-6601

432 10TH ST APT (Range 4A - 4B)

BROOKLYN NY 10598-6605

432 10TH ST APT (Range 5A - 5D)

BROOKLYN NY 10598-6605

432 10TH ST APT 6A

BROOKLYN NY 10598-6605
[download]

This produces the following output:

432 10TH ST, APT 2A, BROOKLYN NY 10598-6601
432 10TH ST, APT 2B, BROOKLYN NY 10598-6601
432 10TH ST, APT 3A, BROOKLYN NY 10598-6601
432 10TH ST, APT 3B, BROOKLYN NY 10598-6601
432 10TH ST, APT 4A, BROOKLYN NY 10598-6605
432 10TH ST, APT 4B, BROOKLYN NY 10598-6605
432 10TH ST, APT 5A, BROOKLYN NY 10598-6605
432 10TH ST, APT 5B, BROOKLYN NY 10598-6605
432 10TH ST, APT 5C, BROOKLYN NY 10598-6605
432 10TH ST, APT 5D, BROOKLYN NY 10598-6605
432 10TH ST, APT 6A, BROOKLYN NY 10598-6605
[download]

It's unfortunate that the data lacks a record separator; that means you have to keep track of what state you are in. If it mattered, I'd do more detection of getting out of sync by verifying we didn't get a city before getting an address.

If one were to use this for anything more than amusement they would quickly discover how fragile the address detection is, and that would lead to a realization of how unfortunate the input data format is.