The code for the BME280 was taken from Adafruit's site and is virtually unmodified. I use the Arduino IDE 1.6.5. I tested it on two different makes of Unos, one Nano, two ESP-01 and one ESP-12. The ESP8266 based boards all read high temperature and low humidity. The pressure reading is fine. Here is an example:
ESP-01 & similar with ESP-12
Temperature = 23.49 *C
Pressure = 1004.99 hPa
Approx. Altitude = 69.00 m
Humidity = 44.80 %
Arduino Uno and similar with Nano
Temperature = 21.15 *C
Pressure = 1005.03 hPa
Approx. Altitude = 68.66 m
Humidity = 52.31 %
Nexus 5 (uses BME 280, but does not display Temp. or RH)
Pressure: 1005.3 hPa
Mercury Thermometer: 20.5C
I tried an SI7021 and had similar problems. The temperature is too high and the humidity low on the ESP boards. While I cannot verify the humidity readings independently, I am sure the mercury thermometer (placed next to the sensor) is correct.
Has anyone else run into this or have any suggestions?