Focusing on the three critical factors influencing laser communication systems operating in marine environments: atmospheric turbulence disturbances, atmospheric attenuation, and optical aberration effects, in this paper, we employ numerical simulation methods to systematically investigate the influence of four typical Zernike aberrations (defocus, y-coma, spherical aberration, and y-secondary quadrupole) on laser atmospheric transmission characteristics and system bit error rates. A comparison of their atmospheric transmission performance with that of the aberration-free state is also presented. The results show that reducing turbulence strength or increasing receiver aperture radius can effectively mitigate the scintillation effect of intensity fluctuations. Among the four typical aberrations, the fluctuation range of the relative change rate of the scintillation index for y-coma aberration relative to the aberration-free state is the largest. In weak turbulence and short-distance laser transmission over the sea, the beam drift caused by these four aberrations is not significant, and stronger turbulence strength or higher weight coefficients lead to more severe beam expansion. The on-axis logarithmic intensity probability density distribution of laser beams with different aberrations approximately follows a log-normal distribution. The skewness (S) and kurtosis (K) of the logarithmic intensity distribution are negatively correlated and always satisfy S < 0 and K > 0. Additionally, we found that as turbulence strength increases, turbulence effects significantly raise the required signal-to-noise ratio (SNR) values to achieve a bit error rate of 10⁻⁹. When turbulence strength reaches a certain level, the impact weights of different aberrations on system performance may undergo changes. These results can provide theoretical references for the design and optimization of laser system parameters in marine laser communication.