I own three Hohner Piano 36s. Two are vintage (pre-gold trim) and one is ten years old and happens to be apart right now.
The white keys on both the new and vintage 36s are about as tight as on any other melodica I own. Only my new Yamaha P-25F has tighter white keys, but the difference is insignificant.
The black keys on the vintage 36s wobble about the same as any other melodica I own. However, the black keys on my newer 36 with the gold trim wobble like crazy. I never noticed this before until I took the newer 36 apart about three weeks ago. The funny thing is my playing was never affected by it and I never noticed it before.
Even the black keys on my new Yamaha P-25F, a precision melodica if there ever was one, wobble substantially compared to its white keys.
So I would say the black key wobble is maybe not such a big concern. But the white key wobble sounds problematic.
I do not see any bushings or spacer plates in my modern 36, although I have not taken the keys off yet. But I can see pretty good in there and there does not appear to be any bushings or spacers.
Sounds like a mystery. The only conclusions I see as viable are: (1) someone banged really hard on the keys for many years damaging the pivot points, (2) the keys or pivot points or melodica frame are warped due to exposure to extreme environmental conditions, (3) the side-to-side play is the result of a factory quality control issue, or (4) there are bushings or spacers in there that I cannot see in mine that have warped, shrunk, or disintegrated.
Does the melodica seal well? If you blow into hard, is there any leakage? If so, I believe it could be an indication of abuse or exposure to harsh environmental conditions. A leaking melodica is not good either.