Dying leaves on my Peace lily

to be honest it is sometimes hard to say, it looks to me as if it has been overwatered and/or has a virus. judging by the white on the top of the soil, i would say that it has possibly been over watered at some stage, even if it has now dried out this can cause fungus in the soil that may cause a virurs, which could have this effect. sometimes you get this white stuff on the soil if it is just old and needs replacing. or if the plant is around too much dry heat (radiators) it could be one of the above reasons or a combination of all of the above. is the soil damp and slimey to touch? if so this would mean it has been overwatered and sitting in water at some stage that has gone stale.

my advice is this; you can do one of two things, if you think it is just a case that the soil is old and needs replacing i would remove all dead and dying bits and dig out the top layer (about an inch should do) and top dress it with new house plant compost, and give it a good feed and keep well away from radiators, then repot it in the spring once it has finished flowering..

if you think it is one of the other things i have said virus and/or overwatering, i am affaid you have little choice but to remove it completely from the pot shake off as much of the old soil as poss and repot it in to fresh and take care not to overwater. if you do this i would also cut off any damaged bits and any flowers damaged or not, so that the energy goes into re-establishing the root system in the new soil. but there is a risk involved in this because it wont like being repotted in the winter but it will die if you don't. good luck.