Since you asked for comments, I'll make a few:
- main improvement is to make better indenting
- if(-d $indir) was unnecessary
- when you do a readdir, this returns only the names (not full paths) and this will include any directories (including the . and .. ones!). It is common to use a grep to filter out the stuff that you don't want.
- always check whether any kind of file operation succeeded or not
- declare variables when you actually use them the first time.
I didn't actually run this so excuse me if I made a mistake.

#!/usr/bin/perl
use strict;
use warnings;

my $indir = 'C:/input';
my $outdir ='C:/output';

opendir(DIR, $indir) or die "can't open directory $indir $!";

foreach my $file (grep{-f "$indir/$_"}readdir DIR)
{
   open IN, '<', "$indir/$file" or die "can't open $indir/$file $!";
   my $new= "$outdir/$file";
   open OUT, '>', $new or die "can't open $new for output $!";

   while (my $string = <IN>)
   {
       undef ($/);

       while ($string =~m/(FINDINGS|COMPLICATIONS)(:)(.*?)(^[A-Z])/sgm
+)
       {
          print "processing $file\n";
          print OUT "$1$2\t$3";
       }
   }
close IN;
close OUT;
}

closedir(DIR);
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update: these "close" statements aren't strictly necessary, all file handles will get closed when your program exists. When you open IN for the next file, this automatically closes the current IN file (if there is one). exit() wasn't necessary, so I took it out.