Or, wow, what a shed!!! You're giving me ideas now..LOL
Have you watered your palms? Even though I'm sure you're allowing them dormancy, they still need water.
Another thing is humidity..do you have a humidifer running in your shed? W/all those tropicals, I'd add one.
Brown leaves usually indicate, too dry soil, not enough humidity or pests.
I'd inspect plants for bugs just to be on the safe side.
Good luck, and again nice shed..Toni

The shed looks like a heaven for mites. They love dry conditions without air circulation. Get some fans blowing and like hopefulauthor said, a humidifier. Your should also spray the undersides of all the leaves with a miticide regularly. Mites will kill your tropicals quickly.

Is this the first you have tried over wintering the plants inside this shed?

Thanks for responding. I have watered the plants. I have one of those stick water measuring meters. I really have to start using it more. I was wondering if I might have overwatered after bringing them in?...Hmmm?
Anyways. I just received 'palm food' in the post. I'll try a little with watered down fish emulsion.
The shed seems to be a great place for plants. It is heavilly painted, floor and walls, so easy to clean. It 'is' a shed, so if I mess it up a bit, well, thats ok. It's insulated and fairly weather tight. This holds in the moisture. In fact, the windows are usually fogged from the moisture. I also mistthe leaves once a week. I'm waiting to see if mould will appear on the walls, ceiling or floors throughout the winter. I have a fan running throughout the duration of my twelve hour timed lights. I have a 'supposedly' safe kerosine heater on a separate timer to come on an hour before the lights, to warm the ballasts as well as plants. I like many, have not read the heaters instructions before use. I should learn how to use its thermostatic controls before winter gets too cold.
I sprayed all of the plants for bugs, before bringing them in and also once they were in. I keep 'neem' on the ready for once a month precautionary treatment. I even put ant traps at the base of my bananas this year. Ants love bananas!
I use the shed because my wife will no longer tolerate that many plants in the livingroom :) Only this fall did I consider the shed. I have just purchased and have started putting some mylar up to reflect back some of the light. I guess it would be wise to rotate on their axis the plants under the lights. Once a month? Next year, i'll improve on everything, as I see their needs. Better, more organized, raised platforms ect. Problem is, the plants I have, will be larger, and i'll probably have twice as many!
i just love after the winter, having all the bananas, figs, palms, jasmines, patchulis, brugs ect, growing out on the front patio here in zone 5!

Your plants could also be suffocating from lack of CO2. With that many plants in the same room the CO2 supply will be quickly used up and the plants will suffer.