There are in fact two different sorts of paint. The first are particles which have blown in the past from flaking wall and ceiling frescos. Then there are some actual dabs of paint on the surface here and there.
In the 16th century, various artists painted life-sized copies of the Shroud. One of them from 1568 (in the Royal Monastery at Guadalupe) is inscribed that it was laid on the Shroud to match the colours as closely as possible. Its paint has been precisely signature matched to paint on the Shroud.
Another practice of the era was to lay newly finished copies on the Shroud with the intention of imbuing them with something of its holiness. There are over 50 copies in France and Spain, with inscriptions that describe how they were laid on the Shroud for this purpose.
McCrone was not allowed personal accesss to the Shroud because, after signing the STURP confidentiality agreement in 1974, he then conspired to do separately related work with ex-King Umberto of Savoy. This resulted in his being dropped from the team. However, in 1978, a friend from the Los Alamos National Lab obtained some surface samples for him on sticky tape.
What McCrone discovered were fine particles of iron oxide. He also found particles of mercuric sulphide, orpiment and madder, all of which are used in paint pigments. And there were traces of parchment dust. He concluded that, since parchment was often boiled down to make a medium for collagen tempera paint, then these were the dusty remnants of a painting process.
He was later proved to be correct, but not in the way that he supposed. This particular type of collagen tempera was precisely that which had blown onto the Shroud from 14th-century frescos in the rooms where it had been housed. As for the iron oxide particles, they turned out (along with some strontium and calcium) to be remnants of the original flax retting, which had been brought to the surface by water dousing in the fire of 1532.