I myself have bought many Android devices (oh yes, I am a tech-geek) and I have learned quite a bit from shops and fellow friends. Without much delay, these are what you need to check when you are buying an Android smartphone.
Check for the matching IMEI
To check for IMEI, turn on the phone and type *#06*# on the dialer. The IMEI figure will pops up and counter check with the IMEI on the box. They have to be the same.
This is rather simple. Always check on the accessories in the box and see if everything is there.
Check the phone itself
Turn the phone around and check for the scratches on the body and screen. Even how new the phone is, always recheck more than once.
Test with Android test mode
Turn on the phone and on the dialer, type this: *#0*#. The test mode will pops up and try out all the test modes available. Here, you need to focus more on dead pixels (most common on Android)
Play around with the phone
New battery usually have about 30% to 80% battery in it. Play around with it and try using the touch screen as much as possible to detect any defect. Don't forget to try on the buttons as factory defect is possible.
I hope that these five methods will help you in choosing the right and problem-free Android device whenever you are planning to get one. Do you any other methods? Feel free to share with me and the rest of the readers by replying below!