I didn't do many residential inspections but my previous boss started his company as a home inspection company and it blossomed into a general consulting practice and he still did the home inspections regularly. A few things he passed on to me.
-Get setup with realtors as their go-to engineer for inspections, they'll pass you a lot of work.
-Setup standardized forms that cover the common items you see. A lot easier to check off a box than write out notes.
-Make sure you clearly distinguish that you're not practicing engineering. Some states will even go so far as to say that you can't even claim that being an engineer means you provide a higher standard of care or otherwise gives you a leg up over a non-engineer home inspector (I completely disagree with this).
-Get your inspections down to an hour or so for a typical home. You'll have trouble being competitive otherwise. Bill for travel time and inspection as a lump sum.
-Pictures, so many pictures. Keep plenty of records of everything for many years.
-Lawsuits ahoy! Have a solid contract that limits your damages to your fee only. Abandon ship and refund that fee at the first sign of trouble. Be prepared to have to fend off frivolous lawsuits on occasion. Also, clearly specify that your scope is limited to visible items only.
-Overall it's a hard area to make money. My boss would often mention he was considering not doing home inspections anymore (at least when we were busy).
All that said; I felt other than odd jobs when not busy, it wasn't worth it to setup a business where residential inspections was the main focus or even a major component. Still, I know a number of engineers who do this regularly so it can be done. I'm sure google will turn up a lot of other details.
As for structural specific inspections, I've done plenty of those and find them far more rewarding/profitable than residential inspections and much less risky. Plus they often open doors to full structural design repairs. The only downside is they're not as available as residential inspections and if they do devolve into lawsuits they can potentially be very big (think career ending for some of the most disastrous ones). So maybe not the best place to start out as a new PE (but not impossible).
Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries