Not a great improvement on the other solutions (below). However, making a single structure saves space and allows for a way to easily see things in the debugger (as shown). Also, no need to scan the list again to obtain the max length.

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

my $maxLen = 0;

my $aline = qq~an interesting line of text I would like to scan I see 
+I see I see~;

my @regexes = (['first',qr/should fail/,0] , ['second','like',0] , ['t
+hird',qr/I/,0] , ['fourth',qr/scan/,0]);

sub niceOutput {for(@regexes){ printf "%-${main::maxLen}s %30d\n", $_-
+>[1],$_->[2] if $_->[2] > 0} } 

sub resetRegexes {for(@regexes){$_->[2] = 0}}

sub rexyScan {my $Len = 0;  for my $n(@regexes){ ++$n->[2] while ($ali
+ne=~m/$n->[1]/g); $Len = length $n->[1]; if($Len > $maxLen) { $main::
+maxLen = $Len } };  }

&rexyScan;
&niceOutput;
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Debugger shows @regexes:

main::(-e:1):    0
  DB<1> @regexes = (['first',qr/interesting/,0] , ['second','like',0] 
+, ['third',qr/I/,0] , ['fourth',qr/scan/,0]);

  DB<2> x @regexes
0  ARRAY(0x569bf962c388)
   0  'first'
   1  (?^u:interesting)
      -> qr/(?^u:interesting)/
   2  0
1  ARRAY(0x569bf95f6650)
   0  'second'
   1  'like'
   2  0
2  ARRAY(0x569bf95f68d8)
   0  'third'
   1  (?^u:I)
      -> qr/(?^u:I)/
   2  0
3  ARRAY(0x569bf95f6428)
   0  'fourth'
   1  (?^u:scan)
      -> qr/(?^u:scan)/
   2  0
  DB<3>
[download]