The single most common preventable failure is running DRC against a tool's default rule set rather than the capabilities of the fabricator you are actually ordering from. Default rules are usually conservative for trace and space and quietly permissive elsewhere, particularly on annular ring, minimum drill, and solder-mask expansion.
Before verifying any layout, automated or not, pull your fabricator's current capability document and encode it: minimum trace width and clearance for your copper weight, minimum annular ring, minimum and maximum drill diameters, minimum mask sliver and mask-to-copper clearance, board edge clearance, and the layer stackup you actually ordered. A clean DRC against real fab constraints eliminates the entire geometric failure class in one pass, and it is the only gate here that fully automates.
One point specific to automated routing: check via count and via type against your fabrication tier. AI routers optimise for completion and can be liberal with vias, and a design that needs blind or buried vias when you budgeted for a two-layer through-hole board is a costing failure, not a geometry failure, so DRC will not flag it.