To answer your question, yes it does go down to 0.01 inches, which is great!. I too have noticed that it will overestimate in periods of heavy rainfall. This is counter-intuitive from what one what normally expect from a tipping bucket style rain gauge, which tends to underestimate heavy rainfall. It seems to perform very well in light rain events, but can sometimes be as much as twice what I record in my standard plastic COCORAHs rain gauge.
Overall, I've been very pleased with the 1035 model. Most of the parameters (temperature, dewpoint, wind) are "spot on" with our local ASOS, only about 6 miles away. Mine did finally develop the "humidity stuck at 98 percent" problem that has been addressed and I'm waiting for one of the newer 5-in-1 sensor packages, hopefully in the next few days. Enjoy your Acurite station, I give it an overall excellent rating, certainly much beyond the Oregon Scientific unit I used for 5 years.
Chris
moreheadcityweather.com