Reverse washing soda buildup on stainless steel
If you use tap-water together with Sodiumcarbonate, chances are that the residue is Calciumcarbonate (unless your tap-water is very soft).

Calciumcarbonate is significantly less soluble in water, but can be dissolved in acid. I would try to put a bottle/arm in a hot 5% solution of acid (acetic acid is fine, personally I would prefer citric acid) to see if any (small) gas-bubbles are formed at the residues. If it does, it is carbonate and can be removed in an acid bath.

If not, the residues could be glue from the labels, and getting rid of this is probably more complicated.