You should enable the warnings and strict pragmas at the beginning of your code.

#!/usr/bin/perl
use warnings;
use strict;
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      7 use subs qw(
      8 error_exit
      9 usage
     10 precheck
     11 generic_check
     12 perl_module_check
     13 print_ok
     14 print_notok
     15 print_info
     16 print_verbose
     17 );
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You don't really need to use the subs pragma. The usual way to predeclare subs is to use the sub function:

sub error_exit;
sub usage;
sub precheck;
sub generic_check;
sub perl_module_check;
sub print_ok;
sub print_notok;
sub print_info;
sub print_verbose;
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     21 @Default_Tools_List = (
     22    [ 'gzip'        ,'app', '' , 'generic_check' ],
     23    [ 'gunzip'      ,'app', '' , 'generic_check' ],
     24    [ 'tar',        ,'app', '' , 'generic_check' ],
     25    [ 'tr',         ,'app', '' , 'generic_check' ],
     26    [ 'date'        ,'app', '' , 'generic_check' ],
     27    [ 'ps',         ,'app', '' , 'generic_check' ],
     28    [ 'cat',        ,'app', '' , 'generic_check' ],
     29    [ 'id',         ,'app', '' , 'generic_check' ],
     30    [ 'echo'        ,'app', '' , 'generic_check' ],
     31    [ 'pwd',        ,'app', '' , 'generic_check' ],
     32    [ 'chmod'       ,'app', '' , 'generic_check' ],
     33    [ 'ln',         ,'app', '' , 'generic_check' ],
     34    [ 'cp',         ,'app', '' , 'generic_check' ],
     35    [ 'rpm',        ,'app', '' , 'generic_check' ],
     36    [ 'clear'       ,'app', '' , 'generic_check' ],
     37    [ 'dirname'     ,'app', '' , 'generic_check' ],
     38    [ 'df'          ,'app', '' , 'generic_check' ],
     39    [ 'Carp'        ,'perlm', 'Perl Module - Carp', 'perl_modul
+e_check' ],
     40 ) ;
     41 
     42 
     43 $Tools_Hash = \@Default_Tools_List ;
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You are only using  @Default_Tools_List twice. You can assign the array reference directly to  $Tools_Hash. You should also use code references instead of strings for the subroutines. (Also  $Tools_Hash is an array not a hash.)

my $Tools_Hash = [
   [ 'gzip'        ,'app', '' , \&generic_check ],
   [ 'gunzip'      ,'app', '' , \&generic_check ],
   [ 'tar'         ,'app', '' , \&generic_check ],
   [ 'tr'          ,'app', '' , \&generic_check ],
   [ 'date'        ,'app', '' , \&generic_check ],
   [ 'ps'          ,'app', '' , \&generic_check ],
   [ 'cat'         ,'app', '' , \&generic_check ],
   [ 'id'          ,'app', '' , \&generic_check ],
   [ 'echo'        ,'app', '' , \&generic_check ],
   [ 'pwd'         ,'app', '' , \&generic_check ],
   [ 'chmod'       ,'app', '' , \&generic_check ],
   [ 'ln'          ,'app', '' , \&generic_check ],
   [ 'cp'          ,'app', '' , \&generic_check ],
   [ 'rpm'         ,'app', '' , \&generic_check ],
   [ 'clear'       ,'app', '' , \&generic_check ],
   [ 'dirname'     ,'app', '' , \&generic_check ],
   [ 'df'          ,'app', '' , \&generic_check ],
   [ 'Carp'        ,'perlm', 'Perl Module - Carp', \&perl_module_check
+ ],
   ];
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     59 %precheck_stuff = ($KSH, $PERL);

    220     for $ent (@precheck_stuff) {
    221     if( ! -f $ent ) {
    222         print_info "$ent not found\n" ;
    223         $ret = 1 if($ret == 0);
    224     }
    225     }
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The hash  %precheck_stuff is never used after you assign to it. The array  @precheck_stuff is always empty.

     93     my @more_paths = split(/\s+/, $more_paths);

    113     my @extra_tools_tochk = split(/\s+/, $extra_tools);

    128       push (@extra_tools_tochk, split(/\s+/, $l));

    138     my @exclude_checks = split(/\s+/, $exclude_list);

    146     my @implicit_checks = split(/\s+/, $implicit_list);
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You probably want to use  my @array = split ' ', $variable instead so that  $array[ 0 ] will always be non-empty.

     92     chomp($more_paths);

    112     chomp($extra_tools);

    121     chomp($tools_from_file);

    137     chomp($exclude_list);

    145     chomp($implicit_list);
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These variables do not need to be chomped unless the user is doing something really weird on the command line.

    115        push(@{$Tools_Hash}, [ $elem, 'app', $elem, 'generic_ch
+eck']);

    131        push(@{$Tools_Hash}, [ $elem, 'app', $elem, 'generic_ch
+eck']);

    154         push(@{$Tools_Hash}, [ $elem, 'app', $elem, 'generic_c
+heck']);
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Again, the fourth element should be a code reference instead of a string.

    175 foreach $component ( @{$Tools_Hash} ) {
    176      my $entity = $component->[0] ;  # first thing is the enti
+ty to check.
    177      if($things_to_check{$entity} ==  1 ) {
    178      $check_function = $component->[-1] ; # last thing is the 
+function to check.
    179      $ret = \&$check_function($entity, splice(@{$component},1,
+-1)); #rest of the inbetween things are args to function.
    180      }
    181 }
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I would use shift for  $entity and pop for  $check_function so you don't have to use splice in the function call.

for my $component ( @$Tools_Hash ) {
    my $entity = shift @$component;  # first thing is the entity to ch
+eck.
    if ( $things_to_check{ $entity } == 1 ) {
        my $check_function = pop @$component; # last thing is the func
+tion to check.
        my $ret = $check_function->( $entity, @$component ); #rest of 
+the inbetween things are args to function.
    }
}
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    240     print_info sprintf "%-${cf_flen}s", $show_user ;

    282     print_info  sprintf "%-${cf_flen}s", $show_user ;
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You shouldn't use string interpolation in sprintf format strings.

print_info sprintf '%-*s', $cf_flen, $show_user ;
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