The basic solution is to wrap all top-level code that isn't inside a subroutine in a new sub, and then fixing all the problems with global variables.

In this case, something like:

use strict;
use warnings;

main();                                                # <----- change
+ here

sub main {                                             # <----- change
+ here
    my $foo = 5;
    
    print "Content-type: text/plain\n";
    print "Content-disposition: inline; filename=foo.txt\n\n";
    
    printf "Package: %s\n", __PACKAGE__;
    printf "[%s] Before: %s\n", $$, $foo;
    badness(5);
    printf "[%s] After: %s\n", $$, $foo;
}                                                      # <----- change
+ here

sub badness {
    my $val = shift;
    printf "[%s] badness: %s\n", $$, $foo;
    $foo += $val;

}
[download]

That will not run, so we need to fix the reference to $foo in badness:

use strict;
use warnings;

main();
main();
main();

sub main {
    my $foo = 5;
    
    print "Content-type: text/plain\n";
    print "Content-disposition: inline; filename=foo.txt\n\n";
    
    printf "Package: %s\n", __PACKAGE__;
    printf "[%s] Before: %s\n", $$, $foo;
    badness(5, $foo);                                  # <----- change
+ here
    printf "[%s] After: %s\n", $$, $foo;
}

sub badness {
    my $val = shift;
    our $foo;                                          # <----- clever
+ trick here(*)
    local *foo = \shift;                               # <-
    printf "[%s] badness: %s\n", $$, $foo;
    $foo += $val;
}
[download]

Real-life scripts will probably be harder, so make sure to run perl -c your_script.pl early and often :^)

Update: As ikegami pointed out, using my $foo = shift in badness runs, but it doesn't act the same. The (*)clever trick suggested by ikegami is a good way to circumvent that. Later iterations should probably move to a more functional approach, by making the subroutines free of side effects.