if you have multiple pieces on top of each other,
i would suggest bind / work on them one by one,
hide the others first so you see which piece is not working correctly.
im not very familiar with lego animation rigs but i would imagine some (if not all)
pieces work better with just setting parent to appropriate bones,
instead of weight binding-
since plastic pieces of lego dont really deform they only rotate.
though my instinct tells me this is more of a structure (parent relations)
problem with your bones (head bone twisted like that after setting something up)
if something suddenly pops out of place after you set parent,
try 1) set parent - relative
2) clear scale, rotate on the objects before setting it up. (ctrl-A)
sorry this is a mess just a couple of things you can try.