Dendrobium-Phalaenopsis Care - Akatsuka Orchid Gardens, Volcano Hawaii
This looks like the Phal type Den. Attached is a link to some growing instructions. It does sound like you could have spider mites if you are seeing webs.
They like fairly good light and if not mite damage, ithe spots can also happen if water is left on the leaves in cool temps. This link gives comprehensive info on their care. If new growths are forming, it may be a good time to repot in a medium with less moss as the roots need to breath a bit. They do not like over potting.
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