maulydaft: Welcome to All Things Plants. I hope you've had time to visit a few of the wonderful forums here and that you enjoy learning and sharing with the rest of us!
I'm not a plant expert ... just lucky enough to live in a warm and humid area where many plants seem to grow well without much assistance from me.
Osmanthus fragrans is a landscape shrub here in some areas of Florida. I don't grow it but I agree with Ann that the spots on the reverse of the leaves in your photo look like scale insects forming. I'd do as she suggested and use Isopropyl Alcohol (common rubbing alcohol). I use it for scales and mealy bugs by dipping a q-tip in the alcohol and rubbing it on the leaves and stems to remove the critters. The webbing indeed sounds like spider mites. I've heard they are extremely hard to control and they will definitely spread to other plants so hopefully you can get rid of them before they do too much damage. Check your local nursery or garden center for Insecticidal Soap Spray for house plants which works well for a few different pests:
http://www.google.com/#q=Insec...
As threegardeners stated, the browning of the leaf tips is more than likely due to lack of humidity. Misting should help and another way to raise humidity is to place the pot on a tray of moist pebbles. You don't want to have the plant sitting in a pool of water, so as the water evaporates add just a little more to keep the pebbles moist.
If it were my plant the first thing I'd do is remove it from the pot, wash off all soil and re-pot it in a clean, well draining potting medium. The soil you are using could very well be the problem, as well as the frequent watering. Many commercial potting soils are extremely heavy, drain poorly and hold way too much water. In my opinion watering 2-3 times a week is way too often. Once every week to week and a half should be sufficient, especially during the winter months when plants are in sort of a resting period. I never have trusted the sticking the finger an inch or two into the soil to test for moisture because the top layers of soil could be dry while the deeper soil could be very soggy and if you have extremely wet soil around the roots they will quickly rot and the plant will not survive.
Regarding the couple of Miracle Gro fertilizer spikes ... um, that may have been overfeeding, especially in October when plants are beginning to go into a dormant type period.
I'm also wondering about the cool temperatures of the room where your plant is located. Does it get any cold draft from the window? Osmanthus fragrans likes heat and humidity so you might want to try a warmer location in the house.
Here is a link to more information about the Fragrant Olive:
http://www.floridata.com/ref/o...
Again, Welcome to ATP!
Lin
Anyway, that was the first plant I prevented from dying! Perhaps a bit too confident I bought over $100 worth of plants (on sale too!) and now I'm starting to worry.
