Aren't there flight restrictions on experimentals -- like you can't fly them over densely populated areas (like cities and downtowns, etc.)
No. Experimental aircraft require the same airworthiness cert that factory-built aircraft do. They are every bit as safe.
"All Amateur-Built/Homebuilt airplanes must be registered with the Federal Aviation Administration (FAA). These airplanes must be inspected by an FAA Inspector or a Designated Inspector before an Airworthiness Certificate can be issued. This is a fairly rigorous process. The builder(s) must provide logs of when, where and how construction took place, along with supporting documents and photographs. If the aircraft passes this inspection, a pilot must fly between 25-40 hours of test flights in specific non-populated areas to make sure all components are operating properly. Only after that test time is flown may passengers be flown in the aircraft.
"In addition, an amateur-built airplane is subject to major condition inspections every 12 months, the same as small production aircraft."
found at: http://www.eaa.org/education/homebuilt_faq.html .
Nope - what fourpeas said. Some of the experimentals are marvelous machines that have me in awe. If I were a floatplane pilot, I'd build me a Murphy SuperRebel. If I wanted a pocket rocket, I'd build a 300+hp Glasair (not the Lancair, though, the straight nose strut looks funny).