A new deep H i survey of the galaxy Messier 33 is presented, based on observations obtained at the Dominion Radio Astrophysical Observatory. We observe a perturbed outer gas distribution and kinematics in M33, and confirm the disk warping as a significant twist of the major axis of the velocity field, although no strong tilt is measured, in agreement with previous work. Evidence for a new low-brightness H i component with anomalous velocity is reported. It harbors a large velocity scatter, as its kinematics both exceeds and lags the rotation of the disk, and leaks in the forbidden velocity zone of apparent counterrotation. The observations also reveal wide and multiple-peak H i profiles that can be partly explained by crowded orbits in the framework of the warp model. Asymmetric motions are identified in the velocity field as possible signatures of a lopsided potential and the warp. The mass distribution modeling of the hybrid Hα–H i rotation curve favors a cuspy dark matter halo with a concentration in disagreement with the ΛCDM dark halo mass–concentration relationship. The total mass enclosed in 23 kpc is 8 10^10,M⊙, of which 11% are stars and gas. At the virial radius of the cuspy halo, the resulting total mass is 5 10^11, M⊙, but with a baryonic mass fraction of only 2%. This strongly suggests a more realistic radius encompassing the total mass of M33 that is well smaller than the virial radius of the halo, possibly comparable to the size of the H i disk.