Android JSON Data interpretation
It'd make sense that accuracy of 16 means there is a 68% chance of being within the circle of 16m radius centered on the reported latitude and longitude, as that's what Android’s getAccuracy() method returns. Similarly, the vertical accuracy (which is often 2 for me as well) would make sense as 68% of ±2m (from getVerticalAccuracyMeters). There isn't any documentation that I can find of the format, so it's hard to be sure.

GPS is normally less reliable in altitude than latitude/longitude, but a lot of phones (mine included) have barometric altimeters, which can give much more precise altitude if calibrated (which Google may be able to do from e.g., weather stations).

All that is well in theory, but looking at own Google Takeout data, it appears altitude is off by ~30m (way more than the ±2m it'd be claiming). [Update This is probably the difference between WGS84 altitude and MSL; see http://www.esri.com/news/arcuser/0703/geoid1of3.html for an explanation and http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm96/intpt.html for a calculator.] And is updated infrequently (it's been showing the same value for me for hours over a bunch of records, and given I haven't traveled anywhere, but you'd expect random variation if it were raw GPS numbers).

I wouldn't assume the correctness of any of this data. Keep in mind what it was gathered for — mostly for statistical aggregation to show you relevant places, ads, etc. None of that requires any given point to be correct. Indeed, in my history, I've got a few points which are accuracy of 1524304 — so, errr, 68% confident which quarter of the globe I'm in?