Some people believe that it has problems. Other people don't believe that. Apparently, Brian Greene is one of the people who don't believe that it has problems, because he used that approach in his book and in his NOVA series. And, apparently Taylor and Wheeler are two other people who didn't believe it has problems, because they used that approach in Example 49 (pp. 94-95) of their "Spacetime Physics" book.[...]
This approach to constructing a non-inertial reference frame has some well-known problems.