I've recently bought a Peace Lily, and the top layer of soil had these small white balls on it...

I'd be very grateful for any advice as to whether this is harmful or not? And whether these are insect eggs, or just some form of mould?

Many thanks...

That's mold. It is harmless to the plant and occurs when non-sterile potting soil is used. I suggest that you scrape off any soil you added to the top of the original rootball. That will eliminate a lot of the visible mold and may make watering easier.

WillC, thank-you so much for your reply, and I'll be sure to check out your book.