I have a solution for new and old versions...read on.
I have recently upgraded to v4.45 for mac but have had the problem that Teri describes with earlier versions. Today I had the same problem when a customer who owed for 2 invoices ($240 & $120) paid only the $240. In the amount box under the customer's name, I changed the $360 to $240, clicked below on the $240 invoice that was being paid and it applied $120 to each invoice. If I was to compete the process by recording the payment, the $120 invoice would appear as paid and the $240 invoice would be partially paid with $120 still owing.
To overcome the problem I double clicked on the $120 in the 'applied' column for the $240 invoice and changed it to $240. The $120 in the 'applied' column for the $120 invoice disappeared. I then recorded the payment, opened the invoices list and the $240 appeared as paid and the $120 appeared as not paid which is the way it should be.
I didn't need to uncheck and recheck "Show paid Invoices" as Teri explained. I couldn't click on the "Apply payment to Invoice" bar because v4.45 no longer has one. My experience with earlier versions is very similar to the post from jadsfeir.
I have the old version still on my mac so I have just experimented and found a solution;
Change the figure in the amount box to the amount being paid,
Click on the invoice being paid,
Click on the 'Apply Payment to Invoice' bar, an 'Edit invoice box' will appear,
Change the 'amount applied' to the amount being paid and click ok.
Then record the payment.
Hope this helps.