Hi Plantgirl,
You actually answered both of your questions. You overwatered your Aloe and before you even realized it it was probably too late to save your root system. You can however save the plant itself (as long as it isn't toooooo far gone.
Remove all damaged (rotted) parts of your aloe (freeze any leaves you remove in a baggie!) and cut the stem back (with a very sharp, sterile knife) to a point where you find no rot or discoloration. Let the plant air dry for 24-48 hours to allow the cut to callous over. Set the base of the plant in some fresh, sandy potting soil. Wait a few days longer before watering the soil, and then water it occassionally, but be very careful to let the soil dry before watering again. A new root system should be developing within a week or two and then you will need to be more conciencious about watering, but always let the soil dry completely before you water again!

For future reference, let your Aloe (or any cacti or succulent) dry thoroughly before you water, wait a day or three, then water thoroughly so that the soil is soaked! Never allow succulents to stand in water!

Your palm needs to have a thorough watering before drying as well, but with most palms you should water as soon as their soil becomes completely dry rather than waiting a few days.

More houseplants are lost because of too much love than from neglect. Overwatering is the main killer of houseplants, followed by underwatering and over feeding.
When it comes to feeding house plants, I normally use half of the recommended strength fertilizer and only apply it half as often. Overfeeding (following the recommended manufacturer portions) will promote very nice new growth but when the seasons change your plant's root system will suddenly not be able to support the "robust" plant itself. Never feed a house plant that isn't actively growing!

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Thank you two for all your help, on these questions and my worm questions from before. I'm glad some super gardners are out there to help out the gardners who are trying like myself.

I did have one followup question on the palm though. I live in So Cal so keeping a humid environment is kinda tough. I keep my palm in the living room for now which is the only room with a heater. No it's not that it's so warm here that more heat isn't needed just that my house is too old to have it.

So should I put the palm in the bathroom where it would be humid a few times a day or in the bedroom where I run a humidifier at night?

Thanks again.