I think you want to lookup the grep() function to search the array. In this case to search for things that don't match -- maybe something like (not i'm assuming 'checked_ids' is an array ref -- if it's not, then have to either split() first or use a different regex check):

  if(  grep( $_ !~ /^\d+$/, @{$INPUT{'checked_ids'}) ){
    # you have bad data
  }
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Actually, re-reading the OP, i think your checked_ids is just a string. In that case,

  my @ids = split (/, +/, $INPUT{'checked_ids'});
  # now check @ids w/grep() using the method above
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Or could check the string for containing just numbers and commas, but the above methods will be preferred (this is less robust and harder to read):

  if( $INPUT{'checked_ids'} !~ /^(\d+(, +)?)+$/ ){
    # you have bad data
  }
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note: not the only, or even best, way to write this regex, but what it's trying to do is match just on set of digits with possibly a comma-space after it.