Short Circuit Detection in wire
This is a short circuit protection circuit simulation I had laying around. The mosfet has a max input spec of 30V. You will have to change V1 to 28V, and maybe add a zener to protect the mosfet gate voltage. May also have to change the comparator supply voltage. V2 is the reference voltage for short circuit detection. Voltage at load below V2 indicates short circuit. V5 is a push button switch that supplies a pulse to start the mosfet. Output of the comparator can be used to drive LED. This circuit checks short circuit at full load, and is preferred over checking short circuit only at startup (what if a short circuit develops while the solenoid is operating?)

To detect open circuit check for ground through the solenoid. This will work as long as 28V supply is off, which is what you want. With 28V supply, op amp input is no longer at ground, so it will show open circuit. The only way to monitor open circuit while 28V is on will be to monitor current drop on the supply line (series resistor and differential amplifier).