The zero-width approximation (ZWA) restricts the intermediate unstable particle state to the mass shell and, when combined with the decorrelation approximation, fully factorizes the production and decay of unstable particles. The ZWA uncertainty is expected to be of O(Gamma/M), where M and Gamma are the mass and width of the unstable particle. We review the ZWA and demonstrate that errors can be much larger than expected if a significant modification of the Breit-Wigner lineshape occurs. A thorough examination of the recently discovered candidate Standard Model Higgs boson is in progress. For M_H ~ 125 GeV, one has Gamma_H/M_H < 10^(-4), which suggests an excellent accuracy of the ZWA. We show that this is not always the case. The inclusion of off-shell contributions is essential to obtain an accurate Higgs signal normalization at the 1% precision level. For gg -> H -> VV, V = W,Z, O(5-10%) corrections occur due to an enhanced Higgs signal in the region M_VV > 2 M_V, where also sizable Higgs-continuum interference occurs. We discuss how experimental selection cuts can be used to suppress this region in search channels where the Higgs mass cannot be reconstructed. We note that H -> VV decay modes in non-gluon-fusion channels are similarly affected.
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