Intelligent reflecting surfaces (IRSs) improve both the bandwidth and energy efficiency of wideband communication systems by using low-cost passive elements for reflecting the impinging signals with adjustable phase shifts. To realize the full potential of IRS-aided systems, having accurate channel state information (CSI) is indispensable, but it is challenging to acquire, since these passive devices cannot carry out transmit/receive signal processing. The existing channel estimation methods conceived for wideband IRS-aided communication systems only consider the channel's frequency selectivity, but ignore the effect of beam squint, despite its severe performance degradation. Hence we fill this gap and conceive wideband channel estimation for IRS-aided communication systems by explicitly taking the effect of beam squint into consideration. We demonstrate that the mutual correlation function between the spatial steering vectors and the cascaded two-hop channel reflected by the IRS has two peaks, which leads to a pair of estimated angles for a single propagation path, due to the effect of beam squint. One of these two estimated angles is the frequency-independent `actual angle', while the other one is the frequency-dependent `false angle'. To reduce the influence of false angles on channel estimation, we propose a twin-stage orthogonal matching pursuit (TS-OMP) algorithm.