If you look at Bob's drawings he depicts his pin as straight and fairly close-fitting through the centre of his cup, whereas the picture below shows my pin is tapered, and the hole in the centre of my cup (yellow and partly cut away in the inset) is much bigger. No circlip was fitted to my pin, it may have corroded away, certainly the cup and its seat were quite heavily corroded. It doesn't seem to need a circlip, the spring is a push-fit onto the diaphragm and into the cup and so lifts the cup off its seat as the valve is opened more than half-way. The pressure of coolant flow from the water pump will also tend to open the coarse-control valve as spring pressure is relaxed.

The first stage is the rubber diaphragm (blue in the picture below) which presses down on the end of the 'pipe' the cup sits in, to completely prevent any flow - the shut-off. As well as this the cup is sitting on its seat (coarse control) and the widest part of the pin is in the hole in the cup (fine control).

As the valve begins to open the blue diaphragm lifts off its seat opening the shut-off, but the cup remains on its seat so the coarse-control valve is still closed. As the pin, attached to the diaphragm, rises through the cup the taper narrows giving a very gradual increase in flow through the valve. This image shows the valve about half open (operating lever about mid-way in its travel) with the fine control fully open but the coarse control still closed.

The third stage is where the valve opens sufficiently to lift the cup off its seat and coolant begins to flow past it giving a rapid increase in flow - the coarse control. The fine-control valve is still fully open and the diaphragm valve is now fully open and the maximum flow is passing through the valve.

If you imagine that that coolant only flows past the raised cup and not through its middle then you would be right in thinking that the first half of valve travel, whilst opening the shut-off valve, does not allow any coolant flow and so is wasted movement, plus the valve won't open as far as it could. Adding washers will cause the pin to start lifting the cup valve off its seat almost as soon as the diaphragm starts moving and so give earlier flow as well as a greater maximum flow, but the washers will block the fine-control valve altogether which will result in there being very little control movement between OFF and HOT i.e. no WARM. Someone else has also opined that if the corroding away of the circlip is not uncommon you wouldn't want a bunch of washers circulating round your engine.

The correct gasket laid over the flange on the heater valve. the hole in the gasket is about the same size as that in the head, with that in the heater flange being very much smaller. This greatly reduces the available area to clamp the gasket and form a good seal. It also allows corrosion to develop on the face of the heater flange which can 'burrow' under through what clamping area there is to cause a leak.

A 'push-off' spring on the cable between the outer and inner clamps. This is nearly fully compressed when the valve is closed ...

... and taking up about 4/5ths of the space when the valve is open. If the spring were stretched out to have a longer free length then it may well push the valve open even more. Some people get hot under the collar (boom boom) about getting the valve fully open, but on both my cars you have to close the heat control at least half-way before getting any noticeable reduction in heat output so I really don't think it is necessary.