I have a Kenmore model 665 and at the end of the cycle we find the soap door open but the soap packet is still in tact undissolved.?

The soap door is sticking. You'll need to take the thing apart and clean it out. Sand rough spots, if possible. Parts that are protected from soapy water can be lubricated.

If that doesn't solve it, there may be a solenoid that allows the door to open that is either faulty, doesn't have power, or is sticking.

Are the dishes clean? Make sure there is enough water. With it in wash open the door quickly to see if both wash arms are turning. If the soap door is opening during the cycle then it is a washing problem that needs to be addressed.

The soap door is sticking. You'll need to take the thing apart and clean it out. Sand rough spots, if possible. Parts that are protected from soapy water can be lubricated.

If that doesn't solve it, there may be a solenoid that allows the door to open that is either faulty, doesn't have power, or is sticking.

How difficult is it to r & r the solenoid?

Are the dishes clean? Make sure there is enough water. With it in wash open the door quickly to see if both wash arms are turning. If the soap door is opening during the cycle then it is a washing problem that needs to be addressed.

Yes the dishes are clean. After resetting the control panel the next load worked fine. I suspect a failing solenoid that works sometimes and fails others. The soap door and latch work smoothly.

If it's a faulty solenoid, you should be able to see it on a wiring diagram. As for replacing it, it depends on the make and model. I'd probably disassemble the door (it is in the door, isn't it), and take a look at how it's installed. If I still felt that the solenoid were responsible, I'd order a new one.

It may be a corroded wire or connection to the solenoid. A corroded connection would present a high resistance to the voltage. That could mean that there may not be enough current to drive the solenoid -- at least not reliably. In that case, simply cleaning the wires and remaking the connection would solve the problem. Alternately, it may be that simply cleaning the moving parts of the solenoid would fix the problem.