Aldehyde-radical reactions are important in atmospheric and combustion chemistry, and the reactions studied here also serve more generally to illustrate a fundamental aspect of chemical kinetics that has been relatively unexplored from a quantitative point of view, in particular the roles of multiple structures and torsional anharmonicity in determining the rate constants and branching ratios (product yields). We consider hydrogen abstraction from four carbon sites of butanal (carbonyl-C, α-C, β-C and γ-C) by hydroperoxyl radical. We employed multi-structural variational transition state theory for studying the first three channels; this uses a multi-faceted dividing surface and allows us to include the contributions of multiple structures of both reacting species and transition states. Multi-configurational Shepard interpolation (MCSI) was used to obtain the geometries and energies of the potential energy surface along the minimum-energy paths, with gradients and Hessians calculated by the M08-HX/maug-cc-pVTZ method. We find the numbers of structures obtained for the transition states are 46, 60, 72 and 76respectively for the H abstraction at the carbonyl C, the α position, the β position and the γ position. Our results show that neglecting the factors arising from multiple structures and torsional anharmonicity would lead to errors at 300, 1000 and 2400 K of factors of 8, 11 and 10 for abstraction at the carbonyl-O, 2, 11 and 25 at the α-C position, 2, 23 and 47 at the β-C position, and 0.6, 8 and 18 at the γ-C position. The errors would be even larger at high temperature for the reverse of the H abstraction at the β-C. Relative yields are changed as much as a factor of 7.0 at 200 K, a factor of 5.0 at 298 K, and a factor of 3.7 in the other direction at 2400 K. The strong dependence of the product ratios on the multi-structural anharmonicity factors shows that such factors play an important role in controlling branching ratios in reaction mechanism networks.