Norman Pritchard, of Mosgiel, said he was concerned the same thing could be happening to others less able to speak out.
The 77-year-old said he had been to the hospital "numerous times" since moving house and had reconfirmed his present address not long before the delivery.
Health New Zealand Te Whatu Ora Southern (HNZ) said there was a processing error, unrelated to the patient management system that has caused problems at the hospital in recent months.
Mr Pritchard was recently prescribed a course of eyedrops for a pre-cancerous growth detected during a cataract operation.
His first prescription arrived at his correct address "good as gold".
When his next prescription appeared to be late, he rang the hospital pharmacy, which asked him to reconfirm his address and told him it had been dispatched.
However, the next day he received a call from the hospital to tell him the delivery was sent to the wrong address.
He was surprised to be told his records needed correcting.
"I said ‘there should be no need to correct the records because my records are correct — where did you get my old address from?’
"They said ‘oh, from the records’."
His eyedrops were then delivered to the correct address.
Mr Pritchard was worried that other people — especially older people — could be in a similar situation but might not have the clarity of mind to follow up with the hospital.
"There’s something wrong drastically there somewhere because I’ve never had this problem before," he said.
The eyedrops, which he was supposed to use four times each day, were meant to be kept chilled.
He assumed the courier, having found he was not at his old address to sign for the delivery, had taken it somewhere for overnight storage.
He was was worried it had not been kept cold.
HNZ Southern group director of operations Hamish Brown said the cold-chain validation for this medicine was not breached despite the delay.
HNZ apologised for the error, he said.
"We have looked into this incident and it was a processing error."
It was not related to the patient management system introduced last November, he said.
The system came under heavy criticism by staff members earlier this year, as reported by the ODT in March.
Among the issues highlighted at the time were the system’s mistakes with patient information, which was sometimes wrong or missing.
HNZ did not answer questions by the ODT last week about if and how the system had been improved.
