The only concern that Kermit Weeks has had in flying his near-exact copy of the GeeBee Z, and a serious one at that, is aileron flutter, which is well believed to be the reason of the original's demise. He had some engineers look at it after the first flight or two he did with it, and found that the aircraft was prone to developing aileron flutter above 240 mph. When the original broke-up in flight, it had likely been going over 300 mph at the time. The plan at least at one time was to add a mass weight balance on the bottom of each aileron to prevent this and allow the aircraft to safely fly above 240 mph, but I believe the plan has since changed, and that when/if flying it again, the plan is just to stay under 240 mph with it. Weeks was also concerned about aileron flutter on his GeeBee R2 (former Delmar Benjamin), and had that one tested as well.
As of last summer attention has been paid to Fantasy of Flight's GeeBee Z, with a number of engine runs and inspections to check that all is healthy and set to go, so that it will hopefully be flown again soon.
For a little technical addition - Kermit Weeks' replica has the exact same airframe design to the original, as that was the goal when it was produced. The replica that was used in the movie Rocketeer, built by Bill Turner in 1978, however, has a slightly larger wing and longer fuselage, to make it more forgiving. That airplane is on display at the Museum of Flight.