When does weak selection produce qualitatively different results from strong selection?
It has been shown that predictions based on weak selection can be different from that on strong selection.
In fact, for rare mutations, each strategy has stationary distribution at the mutation selection equilibrium. The rank of the component depicts the relative prevalence of the available strategies. Yet the rank of the components of this distribution can change with the selection intensity. Thus results obtained under weak selection can not generally carry over to strong selection.

For more details, please refer to Fig. 1 in [1] and Fig. 2 in the supplementary information of [2].

1 Julián García and Arne Traulsen, (2012), Journal of Theoretical Biology, Leaving the loners alone: Evolution of cooperation in the presence of antisocial punishment

2 Christoph Hauert, Arne Traulsen, Hannelore Brandt, Martin A. Nowak and Karl Sigmund, (2007), Science, Via freedom to coercion: the emergence of costly punishment