Sadly, Stewarts aren't immune to their plants suffering from pests. I suspect most come in from Holland on the plants. We have the added complication that our industry is legally not allowed to use pesticides. There's nothing licenced for commercial use, and we aren't meant to use stuff labelled "for home and garden use". We aren't even technically allowed to use plant cleaning products as pesticides, however if we apply them with the intention of cleaning the plant and they have the happy side effect of controlling a pest, that is OK. Daft, but there we are.
So the first pest under discussion is one of the most common: Mealy Bug. This looks like white fluff like little bits of cotton wool stuck to the plant. If you look very closely, you'll see that within the fluff are what look like tiny white woodlice; they are the bugs.
As far as the detrimental effect on the plant, they will eat the flesh of the leaves, leaving yellow patches, as you can see in the photo of an affected Dracaena above. As well as generally weakening the plant, they also excrete a sticky residue known as Honey Dew, which then tends to get secondary fungal infections, and is also a swine to clean off the floor round the plant if it drips on to it.
Saying that, I've known plants live with Mealy for a very long time, so like most pests if managed it's an irritant rather than a catastrophe. So the bit that most people brought here by an internet search are after: how to treat/control it.
1. Keep the plant as dry as you can - this seems to discourage it.
2. Keep the plant as clean and shiny as you can (a leaf shine product or a good wet wipe down). Bear in mind that they are quite easily transmitted to other plants so don't re-use the cloth on other plants.
3. You can also try spraying the plant with diluted washing up liquid, this seems to keep it controlled.
4. Provado, or similar pesticides will also control it, but it seems to be fairly immune to pesticide treatment, especially as the active ingredients keep getting banned and replaced with less effective ones.
5. If you have a major outbreak (and the plants are in a confined area like a conservatory), try a predator bug, in this case called Cryptolaemus (available here), but I'll be brutally honest and say I've had limited success with these, as they tend to either just sit and ignore their prey or fly away!
So in summary, if you find Mealy Bug (or any pest) on your plants, don't panic! First try and physically remove as much as you can, then try the methods above. It's very rare that a leaf-borne pest will kill a plant entirely.