Your posting showed 'system(...); or system(...);' which must be a typo -- perl would call "; or" a syntax error.

Assuming you meant 'system("id...") or system("echo...");' then the problem may be a misunderstanding of what a shell process should normally return: zero if command was successful, non-zero otherwise. Maybe you want to try 'and' rather than 'or' between the 'system()' calls; if the first system calls returns with zero (meaning success), the second will not be executed.

You may also want to simplify your syntax a bit, and use one less system call per iteration (since these tend to slow things down):

open( ERRLOG, ">>c:\\error.txt" );
foreach (@DIR) {
  print "$directory\\$_\n";
  system("echo $directory\\$DIR[$a] >> c:\\dump.txt");
  system("identify -verbose $directory\\$_ >> c:\\dump.txt")
    and print ERRLOG "ERROR: $directory\\$_\n";
}
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