Basic standards - a reasonable level of literacy, numeracy, scientific understanding and so on appropriate to their age (and any SN). Reasonable should broadly correlate to being on a trajectory to be able to get through their GCSEs, but not so prescriptive as to say, for example, that they have to study Soviet Russia in history.
In person assessments annually by a qualified teacher (perhaps more often when the child is first home educated). If they're not reaching a basic standard in HE then clearly it's not working well enough for that child and an alternative approach - a school place - should be required at that moment.
Some children are failed at school, some children are failed in HE. Two wrongs don't make a right, and it doesn't give parents the right to fail their HE child.
HE can be done right, but sometimes it's used as an excuse for letting the child leave education altogether (e.g. gypsy & traveller children who are invariably registered as home educated from age 11, and learn nothing from their often illiterate parents), for full time religious instruction instead of the broad and balanced curriculum they should be getting (e.g. yeshiva, where the pupils are invariably registered as home educated), or letting the child do whatever the hell they feel like ("unschooling" - don't enjoy maths? Sure you don't need to do it...)
Home education can be done well or it can be done badly. If you're worried that your child isn't reaching basic standards of literacy and numeracy, or that your 12 year old thinks the world is flat, or doesn't know what photosynthesis is... then you probably shouldn't be home educating in the first place.