Like her father, her health is not good.
 

Is this correct?

-Like her father, her health is not good.

Arguments objecting to this would be that this sentence is comparing her health with her father, a person; this sentence would mean 'her father is not good' ie he doesn't care about his children etc.

Arguments supporting it would be that as long as the meaning 'Like her father, she does not enjoy good health' or 'Her health, like her father's, is not good' is understood, there's no problem.

What's a native English speaker opinion?

Re: Like her father, her health is not good.
 

It's not grammatical, for the reasons you say. It would have to be: Her health is bad, like her father's was or something similar.

Re: Like her father, her health is not good.
 

Thank you~