What is wrong with this Minolta lens?

Two spring to mind.

Minolta AF 24-105mm (D)

Minolta AF 28-135mm F/4-4.5 Macro (Secret Handshake)

The latter is the best and has a long MFD (unless macro is engaged to reduce it), but the former is a half decent lightweight walkabout.  There are several other options such as the Minolta or Sony 24-85mm F/2.8 which again are both full frame as well as the Tamron SP 28-75/2.8 Di, but many have said the Sony AF SAL 16-105mm DT is a decent option as well and it's APS-C.  Have you done a search on Dyxum and cross-referenced a short list on both the MHohner and Kurtmunger websites in addition to Dyxum?  It would make sense to then sell the 16-50 if you went with the 16-105mm, but the options are many depending on price, format, aperture and focal length.

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Mark @ Sonolta * Photography