What is the significance of the man having no hat (remember this is written in 1861)?

During the time period in question, gentleman wore hats.... not matter their class. The lack of hat, in addition to the broken shoes, allows us to infer that the man Pip meets by the river is no gentleman.

A fearful man, all in coarse gray, with a great iron on his leg. A man with no hat, and with broken shoes, and with an old rag tied round his head. A man who had been soaked in water, and smothered in mud, and lamed by stones, and cut by flints, and stung by nettles, and torn by briars; who limped, and shivered, and glared, and growled; and whose teeth chattered in his head as he seized me by the chin.