Dr Mosley vanished after he was seen leaving the St Nicholas Beach restaurant at lunchtime on Wednesday.
He and his wife had travelled by boat from Symi town, where they were staying in a villa, to St Nicholas beach on Wednesday morning. The return service was not due until 4pm and Dr Mosley opted to walk home on his own.
His wife raised the alarm at 7.30pm on Wednesday evening when she realised he had not returned to their villa.
Eleftherios Papakaloudoukas, the Mayor of Symi, said “many troubling questions” remained about Dr Mosley’s movements on the day he disappeared.
“You can easily get lost and it’s not wise to walk it in the middle of the afternoon in temperatures approaching 40c.
“Why did he leave the beach and his wife and friends?
“Why did he not take his telephone? From the CCTV footage it’s also clear he didn’t stop for a drink in Pedi or take a rest.”
Video showed Dr Mosely walking through the village towards the rocky hills to the northeast.