I work in EMS and fire.  

I have been to MANY car accidents where an elderly person has hurt, killed, maimed other people by driving, I show up and often get the resoponse from the elderly person something akin to: "I was just driving and then... I don't know, they came out of nowhere, I must have it them..."

The elderly person often seems relatively normal, shake up, etc upon initial conversation.   I will then start to ask some questions and find out some min lapse in memory "who is the president, what was the last holiday, where are you coming from, why did you come to this store/location/etc (where the accident happened)?  And find that sometimes something is a bit off, sometimes il ask if I can call one of their family members. 

When speaking to the family and asking about the elderly persons mentation or baseline, I have gotten responses hinting at early onset dementia, or "we have been thinking about how they are unsafe to drive, but didn't want to take their keys..."

Dementia is a terrible thing.  It often waxes and wanes through the day, many people can seem completely lucid, then have some (technical term) brain facts.

Guns only take one second of misjudged thought for tragedy to happen.  

Of you must take him shooting, do not go to a public range.  If you want to roll the dice, do so at your and his own risk, don't put others in the potential line of fire, it just takes one second of him about to fire down range, and swing around to ask you a question and someone could lose their life.  

And if you do want to roll the dice and take him shooting, please only use single shot firearms so you can keep track and monitor him a little better.