I just looked at my weather app (Today Weather), and the report of the current temperature varies by 6°F depending on which data set I choose. I go with the National Weather Service (federal govt).
As far as predicting precipitation, the radar seems pretty good for the next few hours. I press play on it, and it tells me what it thinks the radar will look like for the next 7 hours in 15 mins increments.
I think that predicting the weather beyond a day gets pretty difficult because the weather is too chaotic. The best they can do is to gather data from local weather stations and see how often it rained when they had these same data in the past. So basically, it’s like saying, “When the temp has been 85°F, humidity 62%, wind from WNW at 5 kts, pressure at 1016 mBar, and the date was July 29, it rained 6 times out of 10.”