I have homeschooled in a fairly low regulation state for many years. I absolutely think that homeschoolers should have more oversight than they do here.

At minimum, there should be requirements for the following:

An annual (or better, quarterly) portfolio review that would consist of a report on activities, work samples, and a conversation with parent and student--I envision this as being a non-confrontational meeting and if there are problems that families are given support rather than judgment.

An annual standardized test where scores are evaluated for growth rather than a particular cut score. Students new to homeschooling would take an additional test in the fall (or whenever they start homeschooling). Lack of growth in a particular area would prompt the need for a plan that may involve increased oversight such as meeting monthly rather than quarterly.

An annual physical exam (including updated immunization record)

Parents should have to prove that they are capable of homeschooling at their child's level (or that they have specific plans to outsource and the means to do so). To support this, public schools should be required to allow homeschoolers to enroll in any class they offer.

Parents of high school students should also be required to submit transcripts and course descriptions each year, and these records should be accessible to the student in the same way that the records of traditionally schooled students are.

There should be funding from the state to support these activities.

There should also be the option of using private services to achieve the same ends--equivalent to enrolling the child in a private school.

I realize that these measures won't necessarily capture the kids who are being abused or those families who manage to homeschool under the radar, but it's a start, and certainly more comprehensive than what's going on in many states now.