This is just a theory, but wouldn't a BIG rain gauge be more accurate than a small one? A big mouth would "average" the rainfall over a larger area and be more representative.
You could also make one more precise (or easier to read to 0.1 inch) by using a very large funnel narrowing down into a narrow tube. Say the funnel mouth was 4"x5" (20 square inches), and the tube had an inside diameter of 0.64" (one square inch tube ID).
One inch of rain would fill the tube to 20" deep, letting you read the actual rainfall to 0.1" or even 0.05". (Or you might run the rain into a jug and weigh the jug to get even more precision.)
Please, no jokes about my "big mouth" expertise!
