How large a hole will rain fill with source blocks?

Solution 1:

I had a rain storm which lasted all night and for half the next day, no holes were filled with water of any size. I had a small moat I had dug one block deep, but not yet filled with water, as well as a few one block deep holes scattered around. None of them become filled with water.

I don't think it is implemented.

Solution 2:

Something that can (partially) fill with water during a rainstorm is a cauldron.

A cauldron has approximately a 15.5% chance of being filled with at least one level of water when exposed to one session of rainfall (Tested with 1000 cauldrons during a regular 15 minute rainfall session).

Solution 3:

I don't think that rain can fill holes in the ground, so you were misinformed.
Instead, it can fill cauldrons, but the water inside of them cannot interact with the world properly. (e.g. breaking it won't yield water, endermen won't take damage in them, etc.)