Sounds like most of us are pretty sensitive to what we can and can't say and do, and it does depend on the child, sometimes.
I would never dream of looking at the sell-by dates in any of my (adult) children's fridges, let alone commenting, but they would definitely look at the stuff in mine and comment
The best thing when you want to offer help is to ask. I often stay with my eldest daughter since she had a baby, and I know she appreciates help...but I do check what she wants me to do, if I am doing anything but something very quick and easy (like putting dishes away).
My mother drives me crackers in being over-helpful when she comes here - you can't sit and have a cup of tea with and a biscuit with her for five minutes, because she wants to clear away the cups and plates and wash up for you.