Do doctors use any special criteria when deciding whether or not an elderly patient should undergo chemotherapy?

Yes. There is always an evaluation to decide whether chemotherapy will have benefit at any age. The same goes for the elderly. In general, something called "performance status" is a major deciding factor. Also one must evaluate the potential benefits of chemotherapy based upon a person's age and expected longevity. Surprisingly, many elderly patients with a good performance status do quite well.
Case-by-case basis. Every situation is different, and every decision for something as serious as chemotherapy is made on a case-by-case basis. The basic question is this: is there a realistic chance that the chemo will prolong the patient's life, and improve the quality of life, without making things worse? Or to put it another way: do the potential benefits of the proposed chemo treatment outweigh its risks?