Why is the radar low res and only shows a small area?

NOAA does have a higher res national radar but it is considered experimental right now. You can take a look at the NOAA website at http://www.srh.noaa.gov/ridge2/ The app does support the new radar right now, except if you download through the Amazon app store. So make sure to get the app through the Play Store if this feature is important to you. To enable the new radar, go into the app settings and to the radar section where you can select it.

Why does the radar show activity, often blue dots, even when there is no rain or snow?

You may be seeing radar noise, or ground clutter. You can read more about it at http://www.srh.noaa.gov/jetstream/doppler/radarfaq.html#everything.

Why is the experimental radar blank? There are only grid lines or nothing at all?

This is a Google Maps problem of some kind. Try rebooting your device and make sure you don't a problem with Google Maps on your device in general.