I don't know how I did not notice this before today, the appliance whip from the hot water tank is not directly grounded to the disconnect, at least not to the ground terminal inside the box.
It is screwed to the wire lock nut on the bottom of the box.

Is the box even grounded to the ground lug through the ceramic plate everything is mounted on?

When the plumber changed the hot water tank a few months ago, he must have left the wiring the way it was, it appears to have been this way for a very long time. Is there any reason this should stay like this?

There is also tape on one of the hot wires, so I would like to shorten the whip, removed the taped section of wire and connect the ground to the ground lug.

 

If there is a ground lug inside the box then it should be used.

In your picture I see the ground wire but it doesn't look like it goes into the whip that's pictured. Is your water heater connected with BX cable ?

 

The BX is used for the whip, the ground is doubled back through the locking connector and then wound around the BX.

The ground in the first picture is from the Line wires.

 

Both grounding conductors should be fed into the box. Inside, they should be bonded to each other and to the enclosure.

 

Since I do not know if the case is bonded to the ground lug, through the ceramic plate (I bet it is, but I would have to remove the box from the wall to see),
Can I use the locking connector pigtailed to the line and load ground, secured to the ground lug?

Thanks guys,

 

The label may tell you the purpose of that stud. I am not sure if it can be used for grounding. I would drill the case and install a ground bar or lug.

 

Can you show us a picture of the ground terminal in the box. The mounting stud that the "Line" ground is connected to is not an approved ground. Both "Line" and "Load" grounds need to be terminated on the ground terminal.

 

This is the only label on the box.
I bet it is older than I am, I think I will just switch it out for a modern box and be done with her.

This should do the trick?

Siemens | 30 Amp General Duty Indoor Plug Fuse Safety Switch, 1 Phase, 3 Wire, 2 Pole With Solid Neutral | Home Depot Canada

 

That sounds like a good idea.

 

You probably don't need a fused disconnect if it is supplied by a 30 amp breaker or fuse. Just an unfused 30 or 60 amp A/C disconnect.