Run the ERC and go through each warning or error. Resolve any that you both decide are not an issue. Look out for:
Nets that should be connected but are named something different (3v3, +3v3 for example).
Nets that are connected that shouldn't be (often due to something being renamed improperly.
Nets that are unnamed (N$1, N$12, etc.). This leads to confusion and error.
Run the DRC go through each warning or error. Watch out for overlapping traces, hole size, component/trace proximity, and general noncompliance.
Make sure there are no airwires.
Make sure there are no isolated sections of the ground plane and that there is one common ground.
Look at each trace junction and make sure there are no interior acute angles or right angles.
Measure the width of all power traces and verify them using the trace width calculator.
Measure all holes and make sure they are the correct size for the component being used.
Compare the pin-out of any large components against there respective datasheets.
Print out the PCB layout on a piece of paper.
Make sure all silk screening is on the top of the board.
Make sure the silk screening