Ignoring, for the moment, your misuse of "system" (please do follow Corion's advice - it's dead on target), you could do it this way (a.k.a. "crude but effective"):

#!/usr/bin/perl -w
use strict;
# This is file1

my $error = 10;
print "$error.\n";
[download]

#!/usr/bin/perl -w
use strict;
# This is file2

print "Before: ";
# Run the first script
do "file1";

my $new_error_value = 20;

@ARGV = "file1";
{
    local $^I = ""; # Enable in-place editing
    while (<>){
        s/(\$error\s*=\s*)\d+/$1$new_error_value/;
        print;
    }
}

print "After: ";
# Run the first script
do "file1";
[download]

Or, if you really insist on using "system":

#!/usr/bin/perl -w
use strict;
# This is file2

print "Before: ";
# Run the first script
do "file1";

system "/usr/bin/perl", qw{-i -wpe s/(\$error\s*=\s*)\d+/${1}20/ file1
+};

print "After: ";
# Run the first script
do "file1";
[download]

Update: Tweaked regex to remove unnecessary parens (just because I'm picky like that. ;)