The first one is Dracaena warnekii 'Lemon Lime'. Recently, there have been a number of them with leaf problems - I think their was a supplier problem in Florida. Are the leaves actually rotting, or just split? Cut off anything that is unsightly or mushy, trim the leaves to a point with scissors if the problem is just on the tips, and wait for new growth to fill in.

The second plant is a dieffenbachia. Cut off all affected leaves - it could be a disease or cold damage or damage from improper watering.

Keep both of these plants on the dry side - let the top of the soil get dry to the touch before watering, then water until extra drains out the bottom and dump the extra. With proper care, the new leaves will be much better looking.