Soil looks very dry. Does the container have drainage holes? I would water and remove the damaged leaves.

Can be caused by a couple of different reasons - air too dry (low humidity), underwatering or especially with dracaenas and spider plants, a reaction to chlorine in the water supply. If you suspect that to be the problem, let the water sit overnight before using to allow the chlorine to evaporate.

If you don't like looking at the brown tips, just snip them off.