Hadamard coding spectral imaging technology is a computational spectral imaging technology that modulates the target's spectral information and recovers the original spectrum by the inverse transformation. Compared with the dispersive spectrometer, this system has the advantage of better signal-to-noise ratio coming from multi-channel detection under low illumination. However, the coding process of this system is inevitability affected by several errors, including the misalignment of the coding template and the detector, scanning error, bad pixels, and so on. These errors would have an impact on the accuracy of the calculated spectrum. In this paper, we propose a unitive spectral reconstruction model under different errors and design an integrated approach to correct the above-mentioned errors simultaneously, including the bad pixel's correction method with window function smoothing, the coding matrix's correction method by using corrected template matrix to reconstruct coding matrix, and the push-scanning offset's correction method including the inversion of line offset correction and column offset compensation, which could achieve better performance with the increase of spatial dimension. Experimental results on synthesized data and prototype tests show that the proposed correction method is effective in both single noise case and multiple noises condition, it is more accurate than traditional corrections in which only data preprocessing is finished.