Transferring an H1B to a company that the government thinks is legitimate is very straightforward. I was just hoping to outline the steps to getting a company considered legitimate. So if you can get your company off the ground and considered legitimate (the hard part) then you can have your visa transferred to that company (the easy part).
There are certainly employment contract issues -- moonlighting clauses, non-solicitation, and non-compete agreements. But those all apply to anyone building something on the side while employed full-time.
I think the point @karterk was trying to make is that it might be illegal for you to do any paid work at all at your own startup (or any other company other than your original employer), regardless of whether your original employer allows moonlighting or not. I'm not sure how H1B works in the U.S., but a lot of countries have rules like that attached to work visas. So until your visa has been transferred to your startup, your startup can't pay you any salary.
"anyone building something on the side while employed full-time." -- but if your on a H1-B you will always be working full-time, atleast in my case.
if you are working full-time and building something that is not even remotely related to your current full-time job, do those contract issues still apply ?
There are certainly employment contract issues -- moonlighting clauses, non-solicitation, and non-compete agreements. But those all apply to anyone building something on the side while employed full-time.