I have had mould and you are right on both counts. It starts in the middle of the bud and you eventually get white hairs inside the bud. Before you see anything though the smell will change, it will become slightly musty and not so yummy. This will increase as the mould eats the bud (and the smell) until it has eaten most of the bud.
This is the point it does the mould equivalent of flowering, which is the white strands you can see. By the time you can see it, it is a very mouldy bud indeed.
Basically if you can taste it when smoking, smell it, or see it, then the bud is very very mouldy and you should not smoke it. Ever.
Some people say you can get those tainted buds and wash them in water until you have washed off all the spores (I would suggest at least 3 rinses after you stop seeing any change in the water) then do something other than smoke them, like extract the THC with butane, or make butter. If the buds are very dense, break them up so the water can rinse more of the bud.
As far as I know the main danger is from smoking them as this can lead to a fungal infection in your lungs and lung disease.