Might be a good idea here to take a look at the book suggested above which covers this in detail. The quote below covers some of this.

From: "What Every Credit Card User Needs to Know"

"What if you make just a partial payment on your credit card account? Suppose you pay $100 of a $200 total on your monthly statement? And you later dispute a $120 charge on your account, after you paid the hundred bucks?
Here are the rules the credit card company is supposed to follow in applying the payment for the purpose of figuring out if you have paid for a purchase you have complained about.
Payment goes first to any late charges on your account, with the oldest late charges being paid off first. Then your money goes to pay off finance [interest] charges, again, with the oldest being paid off first. Next, your payment is applied to any other charges on the account. Again, the oldest are paid off first.
What happens if two or more charges are billed to your account on the same day is not clear from the Fed's regulations.
If you have charged two or more items on the same charge slip, payment would, according to the Fed, be applied to each individual charged item in the same proportion the dollar amount of the unsatisfactory purchase bears to the total amount charged on the slip. For Example: You go out to dinner with a pal and charge the tab for the $120 meal (you old sport, you). Your meal was okay. Your pal gets food poisoning from the steak tartare. You pay your entire bill when it comes in from the credit card company except for $60 to cover the cost of the meal that poisoned your pal. Then, you complain to the restaurant [that was a mistake!, don't wait to scream!].
Here's where the problem with the rules comes in. You can only refuse to pay $30 of the $60 that the poisoned meal cost. Under the Fed rules the money you paid was applied not $60 to the good meal and nothing to the poisoned meal as you might reasonably expect. Instead, it was applied $30 to your meal, and $30 to the poisoned meal.
This is pretty silly. There is no reason the Federal Reserve Board could not have adopted a rule that would have applied all your $60 payment to the good meal and none of it to the bad meal. The credit card companies think that the Fed's present rule is better for them, though, and that may just be the reason it was adopted.
Fortunately, if you follow this book's advice you will not have any problem with this.
Complain to the seller or the credit card company before you pay anything on your account. Then you are protected from this foolish application of the Federal Reserve Bank Board's rules."