You create a parallel path for grounded conductor (neutral) current to flow, because of that:
bonded metallic components that are not intended to carry current under normal conditions can be subject to carrying normal operating current.
Rise in voltage to true ground on bonded metallic components because of voltage drop, this don't happen if what is intended to be "equipment grounding conductors" isn't carrying any current.
First should be failed inspection along with reinspection fee.
You will have a parallel path for neutral current on the raceway and or EG conductor. You will also become part of that path when contact occurs with the raceway.
Loss the neutral connection would cause all the current to flow on the EG.
Welcome. The exact hazards depend on the exact conditions of the installation; they are not the same every time under every failure mode. The worst I would say is a 3 wire feeder (2 hots, ground/neutral) subpanel losing its ground/neutral, if all the branch circuits have un-separated grounds/neutrals in the panel, every single grounded surface will sit at ~120V, waiting to shock/kill someone.
EGCs are only intended to carry current under fault conditions.
as Tom mentioned, failed inspection and re-inspection fees are potentially hazardous to your wallet and possibly your reputation too. Having another electrician look at your install say "What incompetent jackleg wired up this garbage?" is embarrassing, but not nearly as bad as the aforementioned safety hazards.