It could be a spotleaf disease. I have the same symptoms on my cordyline (a 'cousin' of dracaena),although not so serious, and I can't get rid of it myself. I have tried to keep the leaves dry (no spraying on on them)so as to contain the desease, but I don't know what else to do.

I would like to hear of a cure,too!

This is quite common in older corn plants. It is likely due to a fungus or bacterial or viral leaf spot; sometimes it can be a sensitivity to fluoride in the water or to built-up fertilizer salts over the years. Your best bet is to take sharp scissors and trim the leaves, cutting off the worst ones completely, and trimming the edges of any with spots near the edge to make them into a smaller, tapered shape to match the existing leaves. Try not to cut through any damaged parts, and disinfect your scissors with a bleach and water solution when you are done. Eventually the problem may go away, or it may not. Your chances are better if you keep trimming whenever you find a spot so the disease doesn't have a chance to continue to spread.

Just in case the issue is fluoride or fertilizer buildup in the soil, once the weather is warm, take it outdoors and leach it. Pour water on it until it runs through, and repeat several times. Let it drain very well, bring back indoors, and let dry before you water again.

I did a little online research and found this product recommended for your situation. Never tried it so can't vouch for it. Just follow instructions carefully with any spray.

Here is a link that might be useful: spray