Correctly determine if date string is a valid date in that format

You can use DateTime::createFromFormat() for this purpose:

function validateDate($date, $format = 'Y-m-d')
{
    $d = DateTime::createFromFormat($format, $date);
    // The Y ( 4 digits year ) returns TRUE for any integer with any number of digits so changing the comparison from == to === fixes the issue.
    return $d && $d->format($format) === $date;
}

^{[Function taken from this answer. Also on php.net. Originally written by Glavić.]}

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Test cases:

var_dump(validateDate('2013-13-01'));  // false
var_dump(validateDate('20132-13-01')); // false
var_dump(validateDate('2013-11-32'));  // false
var_dump(validateDate('2012-2-25'));   // false
var_dump(validateDate('2013-12-01'));  // true
var_dump(validateDate('1970-12-01'));  // true
var_dump(validateDate('2012-02-29'));  // true
var_dump(validateDate('2012', 'Y'));   // true
var_dump(validateDate('12012', 'Y'));  // false

Demo!

Determine if any string is a date

function checkIsAValidDate($myDateString){
    return (bool)strtotime($myDateString);
}