Regarding the jewish date system. It may be worth noting the following peculiarities, some obvious some not so.
1. Jewish days start at sunset NOT midnight so when converting from a Gregorian date to a Jewish one it might be worth asking if the date/time occurred 'after sunset'.
2. Jewish leap years follow a 19 year cycle which can be calculated like this:
function isJLeapYear($JYear) {
    if ( ((7 * $JYear + 1) % 19) < 7 )
        return true;
    else
        return false;
}
3. During a leap year a new leap-month called "Adar I" is inserted BEFORE the normal month of Adar. 
4. During leap years, Adar is renamed "Adar II". 
5. Adar/Adar II has 29 days
6. Adar I has 30 days
7. Cheshvan & Kislev have between 29 & 30 Days
8. Leap years have between 383 and 385 days. 
8. non-leap years have between 353 and 355 days. 
9 . In a 354-day year, months have alternating 30 and 29 day lengths. 
10. In a 353-day year, the month of Kislev is reduced to 29 days. 
11. In a 355-day year, the month of Cheshvan is increased to 30 days. 
12. Leap years years follow the same pattern, with the addition of the 30-day Adar I as well.