Answered
I believe that if a PDF accessibility report fails due to unicode it can not be fixed through tagging. What can I tell the author the problem is so it can be fixed and create a new PDF for accessiblity? This problem is occuring in In-Design and photo shop.
Some more of my nattering here; but -
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You could use the TouchUp Text tool to select text strings, right click for the context menu & select Properties - where, in the Text tab, you can play with changing font style, color, size & embed status.
However, this approach can be less than optimal.
So, yes, you want to set things upfront in InDesign.
Use a 'generic' font.
Something to look closer at is the use of symbols and special characters (such as those used in equations).
In FrameMaker, these need to be provided from the 'Symbol' font set - these map properly to Unicode.
Check InD for something similar.
Also, check any special characters - you want to avoid use of those that pull from 'Reserved' values.
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fwiw, in Acrobat 8 and 9 Pro there is a Preflight that assesses "searchable" (e.g., font uses glyphs that map to Unicode). A Preflight profile using this is helpful in the identification/locating of that which is not mapping to Unicode within the PDF page content's text. This may be available in Acrobat 7 Pro - worth a look-see, no?
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Of course, always ensure fonts/font subsets get embedded into the output PDF.
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~spelling edit~
Be well...