My father can't sign his name because of arthritis. Can I witness his mark?

Typically a "mark" made by a competent adult will suffice legally for a full signature. It should be witnessed, with the witness signing in full.

you could also have him give you poa so you can handle any finances

If this is for now, get his signature notarized, easy, it depends on the documents, but this would require a notary imo.

I don't know the law but think it would be safer to have two non family members witness Dad's mark

I forgot, if you are selling this to a dealer he will have a notary, most businesses do, I am a notary and did it all the time for my business. Title transfer require notary and get a notary friend or ask the person if this private sale to get one.

Finally, keep forgetting stuff. Okay so most states do not require notarization, but some do, regardless it is the best way to cover your butt. Proof that you are no longer responsible for the car in case new owner does not register the car. Most auto clubs, AAA for instance will do this title transfer, paperwork and notarization for a small fee of nothing. You can also both people go to the DMV and do it there.

Take him to MVD to have them notarize the signature of the sale of a car. I owned an automobile document service company in the 1970s and MVD is quite particular about signatures and witnesses. Check with your MVD.

It's dangerous or at best inefficient to make stuff up -- I see people giving their opinion on this site, of things that are not a matter of opinion. Sometimes law and medicine aren't as black and white as we might wish, but for something like this, you're looking for facts. So when there's an expert around like Heiser, take advantage. Or, for example, if you're concerned about the particular rules of your state, I promise you that the answer to your question is on your state's DMV website -- and that it won't tell you you have to drag your arthritis-ridden Dad physically to a notary or the DMV. Put the extra energy that trip would cost you, into getting a PoA for your dad, so you can continue to help with whatever comes up in the future.

A notary can come to your dad's house. But, whatever his signature looks like would be OK, anyway. My MIL had a stroke on her dominate side and her signature is entirely different. (I have a friend with no hands. I should ask him what he does about a signature.) This conversation reminds of all of the schools that aren't teaching script anymore. :)

With all due respect to Mr. Heiser, DMV of each state have their own regulations and rules about the transfer of automobiles, and I too have a POA for my husband, but could not revoke his driver's license with the State of AZ. They want me to physically bring him to DMV to have his signature notarized by them and to identify himself. Food for thought...