How to tell if I need a neck kit for 21303 WALL•E?
I contacted LEGO and this was their reply (emphasis mine):


  All LEGO® 21303 WALL-E sets produced during or after November 2015 already include the neck stability revision, which includes revised Building Instructions and extra parts.  You can tell the production date by checking the manufacturing code which is usually printed in black ink on the clear tape holding the box together.  If your number is 47(S)5 or higher, your have the revised set.  You can also tell my looking at the Building Instruction number.  This number is printed at the bottom corner on the back cover.  New revised BIs produced from November onwards will have the number 6162870 or 6162871.


Unfortunately my BI number is 6146260, so I guess I have a model with the old neck connection.