I try to avoid the use of $1, $2 etc.

I find it better and easier as far as the coding, to put the left hand side of the regex match into a list context and for example assign $catalog_num directly instead of fiddling with $1!

#!/usr/bin/perl -w
use strict;

my @lines = ( 'Catalog Number:  PAL1001',
              '  Catalog Number:PAL1001',
              'Catalog Number: Catalog Number:  PAL1001',
              'Catalog Number:  PAL1001Catalog Number:  PAL1001',
              'Cat Number:  PAL1001Catalog',
              'Catalog Number: 123PAL100');
              
foreach my $line (@lines)
{
   my ($catalog_num) = $line =~ /^\s*Catalog Number:\s*([A-Za-z]+\d+)/
+;
   
   if ($catalog_num)
   {
      print "$catalog_num\n"
   }
   else   
   {
      print "Bad Line!...$line\n";
   }
}

__END__

PAL1001
PAL1001
Bad Line!...Catalog Number: Catalog Number:  PAL1001
PAL1001
Bad Line!...Cat Number:  PAL1001Catalog
Bad Line!...Catalog Number: 123PAL100
[download]

Update:
When writing if statements like above, you have to consider "truth-ness". $catalog_num is false if that value is undefined or it is numeric zero. And that's a "Bad Line!"

In the above, a valid catalog_num cannot be a numeric zero and so I can just test "if ($catalog_num)" instead of "if (defined $catalog_num)".