Aims:We study two dimensional Fabry-Perot interferometric observations of the nearby face-on late-type spiral galaxy, NGC 628, in order to analyse the ionized gas component of the interstellar medium. Covering the galaxy out to a radius larger than 12 kpc, and with a spatial sampling of 1.6'', we aim to investigate the large-scale dynamics as well as feedback from individual H ii regions into their surrounding medium. Methods: The observed Hα emission distribution and kinematics are compared with auxiliary data from molecular and atomic gas observations, which display many similarities. We decompose the observed line-of-sight velocities into rotational and higher-order harmonic components, and study the role of gravitational perturbations along with that of external triggers which can disturb the kinematics and morphology of NGC 628. We calculate radial profiles of the emission-line velocity dispersion which we use to study the role of feedback from individual H ii regions. Results: We verify the presence of an inner rapidly rotating disc-like component in NGC 628, which we interpret as caused by slow secular evolution of the large-scale spiral arms and oval structure. In combination with auxiliary data, we find indication for that gas is falling in from the outer parts towards the central regions, where a nuclear ring has formed at the location of the inner Lindblad resonance radius of an an m=2 perturbation. Complementary continuum subtracted narrow band images in Hα have been used to identify 376 H ii regions with calibrated luminosities. The mean velocity dispersion for the ionized gas (even when excluding pixels belonging to H ii regions) is almost constant out to 12 kpc, although it varies from 14 to 20 km s-1, with a steady decline in the outer parts. Conclusions: We have found kinematic signatures of radial motions caused by an m=2 perturbation. Such a perturbation may well be responsible for the inflow of material forming the nuclear ring and the inner rapidly rotating disc-like structure. The latter, in turn, could help build a pseudo-bulge in NGC 628. The current paper demonstrates a number of tools that we have developed for building a solid frame work for studying the evolution of structure in spiral galaxies using two dimensional kinematic observations. Table 1 is only available in electronic form at http://www.aanda.org The complete version of the H ii region catalogue (Table A.1) is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/466/905