Biosensing with nanoholes is one of the most promising applications of nanoplasmonic devices. The sensor properties, however, are complex due to coupled resonances through propagating and localized surface plasmons. This Full Paper demonstrates experimental and simulation studies on different plasmonic hole systems, namely various patterns of circular holes in gold films. In contrast to most previous work, here, the challenging situation of optically thin films is considered. The refractive-index-sensing properties, such as sensitive locations in the nanostructure and sensitive spectral features, are investigated. The multiple multipole program provides the complete field distribution in the nanostructure for different wavelengths. It is shown that the spectral feature most sensitive to refractive-index changes is the extinction minimum, rather than the maximum. The results are consistent with theory for perfect electrical conductors. The spectral response is investigated for molecular adsorption at different positions inside or outside a hole. Furthermore, the optical properties of nanohole arrays with long-range and short-range order are compared and found to demonstrate remarkable similarities. Our results help to predict the resonance wavelengths of nanoholes with arbitrary patterns, including short-range order. The results presented here are highly important since they extend and challenge several aspects of the current understanding of plasmon resonances in nanohole arrays. These theoretical models, simulation results, and experimental data together help provide the understanding necessary for the development of efficient biomolecular analysis tools based on metallic nanoholes.