I have a basic strategy for dealing with pests and diseases on houseplants. Try the basics, assess the value of the plant and then treat accordingly.
A common problem that I have is fungus gnats. These annoying but mostly harmless insects breed in the potting soil of houseplants and love soil that is kept continually moist. Obviously the best solution is to make sure pots drain freely, but if they have a large amount of soil or like wetter feet, you will get these annoying fruit fly-sized bugs flying around your house. To solve this, I put a layer of white sand about 1/2 inch thick over the soil surface. This reduced the number of gnats last year by a very signficant amount. And it looked attractive (unless I watered with my favorite fertilizer, then it looked stained. But still no gnats).
Scale is a nasty little brown bug that looks like a brown bump on a succulent or new woody growth on a plant. If you scrape it off with your fingernail (or toilet paper) It should come right off without damaging the leaf. You can usually tell when you have scale because you will have sticky spray coating the leaves or windowsill or furniture. It’s pretty nasty.
For scale, use insecticidal soap (I use a spray variety that I can get at Home Depot for about $3 a bottle, but you can make your own. Homemade doesn’t seem to work as well.) This only works if you spray it constantly(a few times over a course of 3-4 weeks), and it is a mess–obviously spraying something on a plant in the house is a pain. I take things to my basement utility sink and have at them. I use this only on high value houseplants, otherwise they get chucked before the scale creeps to another plant. You have to be vigilant about scale because the moving teenage scales are miniscule and can creep up and kill plants. They can also make plants so nasty that you wouldn’t keep them. My orchids and lemon tree are the most susceptible. Both are infested after I put them out for the summer, but if I control it before I bring them in the house, they are usually fine throughout the winter.
My lemon tree suffers from chlorosis, where the leaves yellow and drop because they can’t get the available iron out of the soil because the pH is screwed up. Periodically (when I remember) I add bloodmeal to the top of the potting soil, which seems to help. One of these days I am going to put the tree in the right mix so this stops happening.
Whitefly and mites are two annoying pests that will spread to other plants. I usually spray with insecticidal soap before I bring plants in for the winter and that seems to do the trick. Last year, I ended up throwing out all of my Fuschias midwinter because they were infested with whitefly. I also lost a schefflera to scale. This winter (knock wood) I haven’t lost anything yet, but there is still plenty of time. I think it likely that I will lose my jewel orchid- it is not looking well.
Rust, particularly Amaryllis Rust (which is properly called something in latin) can be prevented by not buying Amaryllis bulbs that have traces of red on the bulbs, as if they have been marked on leaf edges by a red marker. Amaryllis are also susceptible to the fungus gnats mentioned above.
I usually lose one houseplant per winter to some problem. As with most things, you can minimize your losses by prevention and early detection. And don’t be afraid to throw something away or ask for help. Often, unexplained problems can be dealt with by simply watering more or less (the more common cause of houseplant failure), fertilizing, or moving it to a better, brighter (in rare cases, darker) window. If you see pests, act quickly- with houseplants, you often have to sacrifice one for the good of many if an infestation is serious.