Ok, I'm not sure if this was mentioned but euthanasia and what this guy did are two, completely separate issues. This man murdered his son in a brutal manner. Based on the broadcast, it seemed more like he killed his son to hurt the mother (as others have identified here). Euthanasia is compassionate and doesn't involve the severing of body parts. It's a possibility (?) that he will use the compassionate card in court, but hopefully the judge and jury will be smart enough to see past this. This is not a case of compassionate killing.
If there is prenatal testing for the various illnesses / diseases that cause DD etc., I think it's a couple's right to decided whether they want to keep the child. Children are already a big responsibility and like life, there can be a lot of unexpected things that come up. If you're capable of having kids, you should be responsible for them and not expect others to care for them 24/7. If you are one of those people who have a child with i.e. downs there are many sources in the community that can help i.e. CCAC, Community Services, PSWs etc., as Bandit Bill had mentioned.
I think Bandit Bill said it best - they are human too and should be treated as such. I have a friend who's son was diagnosed with Muscular Dystrophy at birth and he's managed to care for him even though he is infirm and also has an intellectual capability of a 2 year old. I have a lot of praise for those who work with and have to live with this daily - They are the advocates for those who can't speak for themselves. It takes a lot of courage and might to want to give the chance of life to someone who can't care for themselves.
As for the elderly, I'm not sure - I think it varies. This is something children need to discuss with their parents for "when the time comes". Directives are important - however if no directives are in place, I think the person should be kept alive with all means possible. Will this be a burden to our medical system? Most definitely, but what about the people who take cancer treatments? Are we going to deny them their treatment because it would be a burden to our health care system? Of course not.
I can go on here, but there is a lot of grey area in this whole topic of euthanasia/mercy killing/compassionate killing etc.,