You can use regexes to validate user input:

if ($input =~ /^[0-9]+$/) {
    # work with $input here
} else {
    die "Please enter an integer\n";
}
[download]

See also: Scalar::Util::looks_like_number

Checking user input can get pretty "wordy" - this is one area where the Perl code won't be much shorter than the C code. Don't worry about that. Be logical and straight-forward. Remember that you are parsing something that a person is typing - super efficiency is not required - logical thinking and clarity of the error messages is!

If this winds up being a page of code - don't worry about it - again you are running maybe 10 if statements - speed is not an issue here - clarity is an issue.

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

my $prompt = "Enter the start date (mm/dd/yyyy hh:mm): ";

my $line;
while ( (print "$prompt"), $line =<STDIN>)
{
   next if $line =~ /^\s*$/; #simple reprompt on blank line
   
   my ($month, $day, $year, $hour, $minute) = 
       $line =~ m|^\s*(\d+)/(\d+)/(\d+)\s+(\d+):(\d+)\s*$|;
       
   if (!defined $minute) #regex failed initial "laugh test"
   {
      print "illegal format!\n";
      next;
   }
   
   if ($month <1 or $month>12)
   {
      print "got month of $month - must be 1-12\n";
      next;
   }
   
   if ($day <1 or $day>31)
   {
      print "got day of $day - must be 1-31\n";
      next; 
   }

   # more conditions here
   
   #finally try to convert the date to an epoch and see
   #if that works, eg  2/31/2012 should fail... 
   
   #all tests pass, you have a "good date time"

}
__END__
C:\TEMP>commandloop5.pl
Enter the start date (mm/dd/yyyy hh:mm): fjfjf 97609876 afadfa
illegal format!
Enter the start date (mm/dd/yyyy hh:mm): 0/0/2012 99:00
got month of 0 - must be 1-12
Enter the start date (mm/dd/yyyy hh:mm): 1/0/2012 99:00
got day of 0 - must be 1-31
Enter the start date (mm/dd/yyyy hh:mm): I stopped program
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Update: Note that the initial regex is fairly loose:
digit(s)/digit(s)/digit(s)        digit(s):digit(s)
is "close enough" - get the basic syntax in the first regex
apr/2/2012 00:02 is not "close enough".
Once the basic syntax requirements are met, then get into the details of what these various fields mean and what the valid values are for them. I am assuming that you want to be "reasonably" user friendly - and not just "screw you - this isn't exactly what I asked for".

Not really the way to check a date, it's already a lot of code and still far from being correct. Use appropriate module:

use 5.010;
use strict;
use warnings;

use DateTime::Format::Strptime;

my $strp = DateTime::Format::Strptime->new( pattern => '%m/%d/%Y %H:%M
+', );

while (<DATA>) {
    chomp;
    my $dt = $strp->parse_datetime($_);
    if ($dt) {
        say "Parsed: $dt";
    }
    else {
        say "Invalid date: $_";
    }
}

__DATA__
2/21/2012
fjfjf 97609876 afadfa
0/0/2012 99:00
1/0/2012 99:00
02/31/2012 01:55
02/21/2012 01:55
[download]