ok you've got some serious problems - most would be pointed out by use warnings; and use strict;

It would be also nice to know what line is "line 686"

# Grabs each district from all_store array
foreach $dist_only (@all_store_info) {
    my @array = split(/ / , $dist_only);
    my $test = @array; 
    # this returns the number of elements not the last array pos
    # so a 3 element array will return 3

    next if $test < 2; 
    # this will only filter out 1 element lines
    # because $test is the num of elements

    $distlist = "$array[1] $array[2] $array[3]"; 
    # first off you are pulling the 2nd 3rd and 4th elements
    # not 1st thru 3rd ($array[0] $array[1] $array[2]) 
    # this is also string data (contains spaces) not numeric
    push(@dist_list, $distlist);
    #print "$distlist\n";
} 


@dist_list = sort { $a <=> $b } @dist_list; 
#you are sorting string data with the numeric op.
#( "<=>" is numeric - "cmp" is string )  

my %uniq;
undef @uniq{@dist_list};
@dist_list = keys %uniq;
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Clean this up and make it do what you want - add use warnings and use strict and then repost this (pointing out the line number in question. Then we can help.