Can an accelerating frame of reference be inertial? In physics problems, the earth is usually considered to be an inertial frame. The earth has a gravitational field and the second postulate of the general theory of relativity says:

In the vicinity of any point, a gravitational field is equivalent to
  an accelerated frame of reference in gravity-free space (the principle
  of equivalence).

Does this mean that accelerating frames of reference can be inertial?
 A: Accelerating frames are never truly inertial; however, in many situations the acceleration is sufficiently small that we can assume the accelerating frame to be inertial. It largely depends on the scale relevant to the problem.
For example, for purposes of projectile motion, we can consider the Earth to be an inertial reference frame and still model the projectile's path accurately. However, in orbital mechanics, we definitely cannot consider the Earth to be an inertial frame, since it constantly accelerates in its orbit around the Sun.
A: An inertial frame is equivalent to a frame's velocity at any given time. An accelerating frame still has intertial frames for the same reason that we can calculate instanteous slopes of a function. An accelerating frame is changing inertial frames constantly but that doesnt mean it isn't an inertial frame at a given point it time.
A: No. By definition an accelerating frame of reference cannot be an inertial frame of reference.
The Earth is only approximately an inertial frame of reference over sufficiently small distances and times. 
A: I think I understand what you mean. In an inertial frame, an object on which no net forces act, moves with a constant speed along a straight line. On earth this doesn't even approximately hold. 
If you still want to consider this as approximately inertial, the conclusion must be that the earth itself is present (as mass, matter or a potential) inside your frame. In other words, the frame is not equivalent to one that is accelerating, but there is a source of acceleration present within the approximately inertial frame.
