How can you find out when a GE dishwasher was manufactured?
THE ONE I HAVE IS MODEL #GSC3500N10WW
To find out the date of manufacture check the serial number and not the model number. You can check the date of manufacture using the reference table found at http://www.electrical-forensics.com/MajorAppliances/GeDateCodes.html.
Contact GE directly and ask customer service. You may also call Sears as they can order replacement parts for that unit. They might in turn also know about the manufacturing dates.