Regular preventative maintenance is necessary with sizable collections of plants, particularly if there are exposure risks (i.e. new acquisitions, plants coming in from outdoors, etc).
The important thing to note is that, it can take time for these methods to work, and most of them do require regular treatment. Once the pests are visibly gone, you will still need and want to develop a strategy to keep them at bay.
My pest/disease preventative is monthly to bi-monthly application of Neem oil. I like it because it makes the leaves shine, kills insects, and seems to significantly reduce the spread of fungal/bacterial infections. I mix a relatively weak dose with some dish detergent and spray. It seems effective. It does have a pungent odor, but the smell is far more palatable than the bitterants or whatever it is they add to insecticides to make them smell so repulsive.
For more pro-active care, I'll hit plants with some Safer soap if I see scale insects, mealy bugs, or mite damage. I actually don't know whether it's more effective than Neem, but I feel like mixing things up a bit will help prevent the pests from adapting. For fungal or bacterial issues, I keep a spray bottle of cinnamon extract, though I use that very sparingly after finding out the hard way that bromeliads and several other types of plants can't handle even a bit of side splash.
I can't say I've had any major battles with mealy or scale (yet), but I know in my collection, it seems to be mites that find their way in from time to time. Other than that, most of my creepy crawlies are more benign, such as pill bugs, spring tails, fungus gnats, and spiders. I don't generally bother to spray or treat for those. A good flush tends to flood most of them out periodically and keeps those populations in check.