since you are not entering a complete date in the Month or Year field, you cannot use the date validation type.
You have two options:
1) Use numeric validation for the month and year fields. you really only need to validate that the month is between 1 and 12 and the year is a two digit number greater than 10
2) Use select lists instead of text fields for both the month and the year as was suggested back in post 31 of this thread:
by using a select list, you can remove the need to validate those fields since you are giving them the appropriate options to chose from.
The issue of client side validation is completely up to you. Some People like to use client side validation and server side validation together, but it is not necessary.
The difference between the two is when / where they occur.
Server side validation occurs when the form submits to the server. Because it is processed on the server, the client cannot disable it, this means it is a more secure option.