3-4mm probably indicates that you are not absolutely vertical with the drill, or are wobbling slightly..
Try a Post drill if you can get access to one.
hinge rattling would say 2 me that the forstner bit was either 2 big,very dull (blunt) and is moving around or your not drilling it correctly or square!
remeasure the widest point of the hinge accurately,buy a new and sharp forstner bit and look into how u could drill it better,bd3cc had a good point,u cant go wrong with a drill press/pillar drill,failing that if uve access to a decent trade cordless drill and a steady hand and a bit of practise then ul crack it!!
do all of this and if its still not right then u shoulda gone to specsavers!
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