Here are pictures of the infected leaves. I cut them off the plant as soon as I saw them today.
Click for full size
Here are close-ups of the most infected leaf:
Click for full size
What can I do to prevent this from happening to the rest of the plant?
Edit
I may have found the culprit. I found the what looks like a fruit fly right beside a new white patch. I am not sure if it was snacking or had just finished laying eggs. I am actually not sure if it was a fruit fly at all. Here are some pictures:
The first two are the bugs in action. Here is a close up of a bug I caught while cleaning the leaves with soapy water.
Can anyone confirm this is a fruit fly and that it is the bug responsible for the white mess?