Thanks everyone for the replies, very helpful. I moved my overhead lights around to get the flourescent lights away from the scale and moved the LED lights closer to the scale. My home was built in 1917 and I have about ten or more power strips in the basement, so finding an outlet with nothing else feeding off of it is problematic. There is ONE that runs directly to the fuse box over by me drill press, quite a ways away from the reloading area. I can move the scale there if I have to but I really dont want to because when I am loading fixed ammo I will be a long way from my press and I like to load the bullet right after charging each case.
I know just enough about electricity, so I want to confirm my understanding of what I read in the comments. If I buy one of the "noise filters" referred to above,(price around $30) I should be able to use my digital scale on a line which has a tv, laptop, hand held vac and a cable box connected? I can reload the other appliances turned off but they still draw some current. I could also just unplug them as a backup plan when using the scale. 
Please let me know what you think. 
the other issue is "normal" room temperature. The temperature in the basement is about 60 deg in the winter, and about 65 in the summer. Not much I can do other than run a space heater.
Any ideas?

Thanks!
Joe S

I would assume warm air currents might affect digital scales, but even more so the in rush current draws of a furnace, whether it's in the same room or not. Motors draw at least 300% of nameplate rating on startup and even more. Those draws can affect all sorts of things in a home, especially an older home where several rooms can be on the same circuit.
Voltage fluctuations can make major problems with electronic equipment, and the choke wont help those issues. A surge protector (along with the choke) will possibly help, but not sure how much.