Dobson was elected an Associate of the Royal Academy on 31 January 1860, and an academician in January 1872. He was a member of the Etching Club, founded in 1842. In 1870 he was elected an associate of the Royal Watercolour Society, of which he became a full member in 1875. He remained a constant exhibitor, both at the Royal Academy and at the Royal Watercolour Society, contributing about a hundred and twenty pictures to the former and about sixty to the latter. He was appointed a British juror for the Exposition Universelle, Paris in 1878 and was represented there by 3 watercolours. He became a retired academician in 1895, and died at Ventnor on 30 January 1898.