Thanks Dan! I've been enjoying the series quite a bit. I guess development control and enforcement are better suited for TV than policy planning :-D
Knowing a little bit about the British planning system, and the types of incidents that are covered on the show, I don't think a US/Canada version would translate well. The show is really centered on planning enforcement, and not the greater planning process.
In the US, at least, when a project gets planning approval -- usually administrative, such as for a shed, pool or single family house, but often approval by a planning commission for larger projects, depending on the municipality -- a building permit is required. At every stage in the building inspection process, the structure and site are visited by an inspector, are compared to the approved plans. Builders and developers must call the municipal or county building department to schedule inspections at various stages in the development process; they cannot proceed without a particular stage being "signed off", and skipped stages can be costly. For instance, neglecting to have a plumbing inspection completed before drywall is put up, can cost a builder thousands of dollars, since they'll usually be required to pull the drywall off so the plumbing can be inspected.
Any discrepancies are usually caught by the building inspector, who refers the developer to the planning agency for plan revision. "Red tagging", or shutting down work on a project or part of it, will occur if there is deviation from the approved plans. Building permits must be posted in a visible location, and building officials make regular rounds, so if there's construction taking place at a site where building permits aren't posted, it's caught very early in the process.
There are a few parts of the US where building permits and inspections aren't required; usually libertarian-leaning frontier towns in Alaska or the remote West.
In the UK, at least watching the show, it seems like there's no building inspections; these almost-finished buildings that don't get planning permission or which deviated greatly from the approved plans are a surprise to the planners. The UK planners, from a US perspective, seem like part current/development review planner, part zoning manager, and part code enforcement officer.