Beam stabilization is critical in an adaptive optics beam clean-up system to improve the power concentration in the desired area during a period of time. In these systems, the average wavefront slope from a Shack-Hartmann wavefront sensor is widely employed as the feedback of beam stabilization. However, when the adaptive optics system is applied to improve the beam quality of a high-power solid-state slab laser, the “M” shaped aberration at the edge of the slab and the fluctuating intensity distribution of the beam would induce some errors when using the average slope to measure the direction of the beam. In this paper, we present the numerical analysis of beam direction detection errors in solid-state slab laser beam clean-up systems using the average slop. At first, we calculated the direction detection errors with the aberations composed of the first 64 Legendre polynomials using the average slope. Then we measured the wavefront of a solid-state slab laser with a Shack-Hartmann wavefront sensor, and evaluated the influence of the “M” shaped aberration and fluctuating intensity distributions both in the time and frequency domains. It is clear that these factors bring in significant detection errors. Finally, we proposed a method by removing some edge sub-apertures when calculating the average slope.