Many of the dracaena used as house plants have a problem with fluoridated water and virus/fungus/bacteria can show up when they are over watered. See here for more details.
What I see in your pictures that is described in the link is
- "reddish to tan spots with wide, yellow halos" - described as Fusarium Leaf Spot
- most of the tips have been trimmed which is believe is because they died back to fluoride toxicity
Let's do a little check. Is your tap water:
- alkaline pH?
What happens is these plants get potted up in an mixture of peat moss and perlite that starts off with a slightly acid pH. As you keep adding alkaline water with fluoride and the organic content of the soil declines due to the roots turning soil into stems and leaves the pH of the soil changes to be more alkaline.
Good news is that these plants can out grow the fusarium with some help and they respond very well to being cut back hard.
I suggest the following:
- get some top soil, not potting mix. Top soil will have a mixture of clay, sand and organic material that can buffer the soil pH when alkaline water is added.
- sterilize it by layering it on a tray in the oven for 200 degrees for 30 minutes as described here
- take the plant out of the existing pot and ensure the roots are firm which indicates that you do not have root rot. If roots are soft then cut them back.
- remove an inch or two from the bottom of the root ball
- add your sterilized soil and put the plant back in the pot
- cut the plant back at least a foot or more from every stem showing damage. It will look ugly but will bud out
- water with a filter that removes the fluoride
- increase light levels after re potting for a few months
- use a 20-20-20 fertilizer monthly at 1/4 recommended strength during the summer months when I assume it gets more light. If you want you can use a sea weed or other organic fertilizer but they usually cost more and some of them smell
See my answer here for more details on care.