there's nothing much you can check on the spot, it's just like buying phone.....

anyway these are the few things commonly checked on the spot before buying pda;

1. hardware button - make sure all buttons are functioning as it suppose to be
2. screen - make sure no scratches, no dead pixel [very unlikely]
3. body - make sure no scratches
4. phone function - try make some test call to check the clarity of the sound and volume, test the camera function
5. accessories - make sure all accessories is complete in the box
6. warranty - make sure the pda is locally covered [ not advisable to purchase AP pda ]

most important is to apply screen protector before using it !

after purchased test;

1. make sure test all the function e.g gps
2. battery - checked whether it suffer from charging problem, battery life etc etc
3. try to pair with other device e.g bluetooth, usb etc etc

my advise is to read up all 20 pages of this thread to check the common issue with this particular model!

btw Asus is quite well known for its quality product ....

if your device is no longer in warranty period, probably you might want to consider to open up the devise yourself to fix the vibration issue [ could be the vibrator loosen? ]

here's the official service manual of Asus P750 to guide you the process - download it HERE !

Note : do this at your own risk...