What Nathaniel wrote
*"This statement is over ${\mathbb Z}$. I don't know of a rational version of Ranicki's total surgery obstruction, and Ranicki told me he doesn't either."* 
is strictly true in the sense that I had forgotten that I had a manifold interpretation of the vanishing of the rational total surgery obstruction in Proposition 7.7.5 (page 763) of my book on exact sequences in the algebraic theory of surgery (reference [2] below)! So I have now edited my original answer accordingly 

The total surgery obstruction $s^R(X) \in {\mathbb S}_n(X;R)$ of an $R$-coefficient Poincare duality space $X$ can be defined for any ring $R$ with ${\mathbb Z} \subseteq R \subseteq {\mathbb Q}$. In the 1970's Quinn (and others) developed surgery obstruction theories for $R$-coefficient Poincar\'e duality spaces, but these theories have languished both for theoretical and practical reasons (e.g. a lack of examples). Proposition 7.7.5 of [2] does give a manifold interpretation of $s^R(X)=0 \in {\mathbb S}_n(X;R)$, but I am not sure if it is sufficiently geometric for practical purposes.

If anyone is interested in reading more about the total surgery obstruction, here are some documents which are available online:

[[1] "The total surgery obstruction"][1] 1978 paper

[[2] "Exact sequences in the algebraic theory of surgery"][2] 1982 book

[[3] "Algebraic L-theory and topological manifolds"][3] 1992 book

[[4] "The total surgery obstruction"][4] 2010 MPIM lecture

  [1]: http://www.maths.ed.ac.uk/~aar/papers/total.pdf

  [2]: http://www.maths.ed.ac.uk/~aar/books/exact.pdf

  [3]: http://www.maths.ed.ac.uk/~aar/books/topman.pdf

  [4]: http://www.maths.ed.ac.uk/~aar/slides/mpim.pdf