After resolving all other issues I had with my as-new-but used N810 I was left with the backplate where the battery goes having some 'play'. It would move up/down/left/right 2-3 mm - not much but enough to give the whole device somewhat of a 'un-sturdy' feel to it.

Then last night I remembered that I had the exact problem years ago with a Palm Treo 600/650...and the way I fixed it was by folding a piece of paper and putting it inside of the battery lid...so...I just tried it out. I folder a piece of paper about the length of the battery compartment. Slid on the lid..and...the back is now rock-solid

DIY the easy way