The United States Geological Survey (USGS) runs many real-time data streams including water stage data. While the USGS clearly thinks this is worth doing, they provide a succinct reminder to users that, like everything in life, real-time data are not perfect. More importantly, they don't consider this a cause for panic - a cause for later analysis and data revision, certainly - but not panic when initial and public data may be inaccurate. After all, they're measuring events in the real world and not a controlled laboratory setting.
See the FAQ entry for "I frequently kayak the Potomac River and the real-time stage data reported by USGS seem to be too high (or too low). Are the USGS data inaccurate?" their answer.