The Forth Bridge is so big that as soon as maintenance crews have finished painting it, it's time to start again. Thus, any task which can never be completed is said to be "like painting the Forth Bridge".
The world's first steel, long-span, cantilever bridge, opened in 1890, remains one of mankind's greatest engineering achievements. As a modem symbol of Sisyphean labour, however, it's useless. On reflection, starting at one end and painting doggedly towards the other would be a deeply inefficient approach to such an immense and dangerous job.
Sure enough, an inquiry to the Forth Bridges Visitor Centre Trust brought the categorical statement: "The bridge was never painted in that way. Different parts of the bridge suffer different levels of exposure to the elements; the maintenance schedules reflected that."
It's all academic: the bridge is currently having its famous red paint replaced with an epoxy resin expected to last for 20-30 years. In America, incidentally, the equivalent expression is "like painting the Golden Gate Bridge."