Use Design rule check (DRC), Create error reports
Most PCB design packages have tools to check errors, so use them. Check if there are any spacing violations, unrouted tracks, off grid vias, parts or text outside the border.
Check your footprints
When getting your PCB from the manufacturer and start placing components, one of the worst things is to find out that the footprint is wrong. It can be due to wrong pads spacing, the wrong offset for the side pads, wrong size drill holes or even forgetting some pins or the exposed pad.
So it is always a good idea to order critical parts before sending your artwork to the PCB company and get a print of your board at 1:1 scale to check if the parts fit well on your footprints.
You can even print your PCB design to a transparent printer film to check the BGA components or the exposed pads under the package to see if there is an alignment problem.
Check fiducials and test points
If you are going to produce your board with automatic assembly machines (pick and place machines), they will probably need fiducial marks as registration marks for fine alignment of SMT components.
So put some fiducials (at least 2, 3 is optimum), at corners of the board. It is also a good idea to place two fiducials (opposite corners) near to the parts with a high number of pins.
We usually decide test points at the schematic stage to check critical signals but if won’t harm to check again.
Connectors are the most important components that will affect the mechanical design, so be sure you place them on the right side of the board, set the distances well, and consider the mating connectors. Connector to connector spacing is one of the most common errors in PCB designs since we only consider the connector outline in our PCB editor and can forget the mating connector size. So remember the mate may need some extra space on both sides.
Check Silkscreen layers
Check if silkscreen layers are readable, component references are as close as to the associated part and do not forget to add some text about the board name, version etc.
Silkscreen is also good for put some warnings (High voltage, do not touch etc.) and give information about the switch positions (Off, on, reset etc.), meaning of LEDs (3v3, Ready etc.) These will help users or technicians in prototyping and maintenance stages.