Tasteless condition of points in teeth (9)

I believe the answer is:

tattiness

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'tasteless condition of points in teeth' is the definition.
I can't judge whether this definition defines the answer.

'tasteless condition of points in' is the wordplay.
'tasteless condition of' becomes 'tats' (I can't justify this - if you can you should believe this answer much more).
'points' becomes 'tines' (I've seen this in another clue).
'in' is an insertion indicator.
'tats' placed around 'tines' is 'TATTINESS'.

Can you help me to learn more?

(Another definition for tattiness that I've seen is " in poor condition".)

I've seen this clue in the Sydney Morning Herald.

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