1. “Looking round on tube it appears that planes that are not flat are a common problem,”
It is common; but, is it a problem?
2. There is a post on Paul’s blog showing that a #4 plane can flex (so much for flatness).
3. Surfaces with a mirror finish tend to stick. I will never try to have a mirror finish. If I were obsessed with sole flatness, I would use a scraper (like it was done on old machine ways). That would create small pools for the oil of “te rag in the can”.