Grey market items may say things like "not for sale in [your country]" on the box. They may contain labeling that's not consistent with the standard labeling for your country. They might not have certain disclosures that your country requires for certain types of products. Certain features may not work. Stuff like that. They aren't always identifiable though.
At some point I was using Amazon for almost all shopping. Obviously daily is an oxymoron, but it'd happen several times a month.
I can identify grey market items easily. Buy an item in Amazon UK of product X and get version packed to be sold in Italy (with all labels in Italian) or Russian (with all labels in Russian), instead of the UK version. This is because some smart supplier is doing arbitrage.
I've noticed that a significant number of my recent TV/film purchases from Amazon UK looked new on the packaging but had some sort of mark on at least one of the discs, suggesting that something had been handled previously. This seems to be a clear trend over the past 1-2 years that I had never previously encountered. In some cases, it's been obvious enough that I've returned the product, though I also have lingering doubts about whether others with just a small mark might have been me when opening the packet but might have been something else.
I already basically gave up buying anything important and/or fragile from Amazon and now avoid them for almost everything around holiday seasons. Far too many instances a few years ago of things like different sizes of items thrown into a box with obviously inadequate packaging, resulting in damaged electrical items, would-be Christmas presents turning up unfit to give as gifts, and so on. They're pretty good about accepting returns without quibbling much these days, but it's still a huge hassle when things go wrong so often and so avoidably.
It's a shame, because for a while Amazon was a convenient alternative to bricks and mortar stores and carried a wider range of books and TV/film/music than any physical store. I'm glad I supported the better local stores now, and that some of them are still there so I can buy from them instead today.