Does this look like spidermites?

"Simon 420", a question or two below your question has posted pictures of leaves that show damage similar to what spider mite can do to leaves, it may be worth checking them out for future reference.

Those marks on the leaves are not spider mite caused or signs of spider mites., they can be caused by water on the leaves and sometimes also be just normal "blemishes".........no plant will ever have 100% perfect leaves, 100% of the time. Spider mite damage generally looks like tiny yellow/white dots everywhere the mites have sucked the sap out of the leaf. The little black dots are not spider mites either, mites will scoot around and leave webs behind. The dots are hard to identify in the pictures...........if there are only one or two, just squash them. No need to poison your baby plant with sprays because you imagine there is some sort of major plague attack going to happen.

Pest can be super tiny but if you are truly worried. I would do a neem oil mixture treatment on it. Spray on everywhere. I let it sit about 30 mins then rinse off. Then repeat treatment in about 4 days. This generally breaks any pest cycles

Not easy to tell from the pictures, could be, could also be thripse. Have you checked the underside of the leafs? Its good to get some kind of magnifying device like macroscope to tell safely whats going on here. Spider mites are in fact small spiders and will make webs similar to their big relatives.