Problems do occur on first flights...but the frequency and severity of the problems have fallen dramatically over the last few years. I believe this is due to several factors.
One of the largest is the EAA Flight Advisor program. Another is the transistion of the homebuilt industry from a scrounge it situation to the present trend of highly kitted proven designs and interest by most builders to use the best available materials, engines, and accessories.
Since most are familar with the FA program, I won't go over it in detail (you can find more info about the program at the EAA heardquarters site).
In my personal experience as a FA since the inception of the program, I have yet to have a briefed first test flight have a major problem...and most of the few problems are small sensor or instrument problems. And this is one of the items handled by the FA briefing and flight test program.
Before the FA program, I had been involved with a number of first flights starting with my own BD-4 in 1979. First flight was faultless, third flight was very similar to Bob Axsom's as posted earlier (broken prop governor line, overspeed and loss of all oil leading to re-overhauling the engine).
Two of the most memorable bad first flights before the FA program include a Verieze which resulted in a fatality and a RV6A in which the outstanding design of Van's saved the pilot's bacon. In both these cases, standard FA briefing items would have prevented the incidents.
So...the FA program is very important with good results, be sure to use it for your first flights and flight test period.
Deene Ogden
EAA Flight Advisor, EAA Tech Counselor
CFII, CFIG, MEI