"Two weeks' notice" is correct. The notice belongs indeed to the weeks, just as a month of Sundays would be that month's Sundays.
Then again, it would be depend on the usage, and one could be forgiven I think, for thinking of "two weeks" as an adjective modifying the noun, "notice". What kind of notice? The "two-weeks" kind. The author compares "one month's notice", and I'm not sure that's a canonical example, as I would likely say "one-month notice", myself.
What trips me up most often is when to hyphenate and when not to, as illustrated by the above ambivalence.
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