All of our machines log the last 500 errors with time/date stamp. Talk about an invaluable tool for troubleshooting.
Back to the original question "Can someone briefly describe hardware problems that occur in a PLC that an in plant PLC person would repair?"
Speaking only of hardware (not the PLC program) you've got input cards, output cards, communications cards, fuses (depending on PLC) that, CPUs, backplanes (or racks), and power supplies; all of which can fail for any number of reasons. You also may find an input or output card with only one bad input or output point. If a replacement card is not available then moving the wires to an unused input or output and updating the software for this change is also pretty common.