Born at Manly, NSW, son of master builder Robert Wall and Lenna Lorraine Wall, he was educated at the Launceston Church Grammar School and at the University of Melbourne. After two years at the Alfred Hospital he spent 1940 to 1944 in the AIF as a captain in the Army Medical Corp., seeing service in Malaya. During World War Two he was a captain in the AAMC of the 2nd AIF, and served at the 2nd/4th Casualty Clearing Station in Malaya from 1940 to 1941. He also served at the 115th HMH from 1941 to 1944 and 121st AGH, 101st AGH and 102nd AGH. Following his war service he spent a year as RMO at the Children's Hospital, Melbourne and then settled in Launceston where he became the first honorary paediatrician to the Launceston General Hospital and also to the Queen Victoria Hospital. In 1960 he was made a member of the College under Article 37A for his services to paediatrics, and became a fellow in 1974.

Dr Wall was a skilled committee man, and was president of the Tasmanian Branch of the AMA from 1965 to 1966, a member of the Tasmanian branch council from 1964 to 1976, federal councillor of the AMA from 1967 to 1976 and for a time was a member of the federal executive. He was made a fellow of the AMA in 1968. He was president of the Australian Paediatric Association from 1965 to 1966 and was made an honorary life member of the Australian College of Paediatrics. He was a member of the medical council of Tasmania from 1951 to 1953 being president from 1973 to 1983 and it was through his efforts that the Tasmanian Medical Act was brought up to date. He was a director of the Australasian Medical Publishing Company Ltd from 1966 to 1980, chairman of the Medical Benefits Advisory Committee from 1975 to 1983 and a member of the Hospital and Health Services Commission from 1974 to 1977. He served from 1978 on the executive of the Australian Medical Examining Council. He was municipal officer of health in the municipality of St Leaonards and the City of Launceston from 1970 to 1975. He was a director of the Tasmanian Asthma Foundation from 1965 to 18975. He was also director of various propriety companies, including the Tasmanian Permanent Building Society, Gunn Genders Holdings Pty Ltd.

He was married in 1949 to Dorothie Joyce (née Ellis) and there were two sons, Robert and Anthony. Bob Wall had the great ability to see the essential points in any discussion or debate, and to state them with clarity. He always placed service to patients as the highest priority, and was an excellent teacher. In particular he encouraged many others to undertake further study. He had a particular flair for financial matters, whether corporate or in private investment, and was regarded almost as a wizard in this field. His reception of the honour of being made an Officer of the Order of Australia in the Queen's Birthday Honours in 1983 was a fitting reward to a man who gave so much of his talents and time to his profession and to the community.