1. Incorrect dimension of matrices. Matrix multiplication is only defined if the number of columns of the first matrix is equal to the number of rows of the second matrix.
2. Off-by-one errors in loops. Loop indices may not be correctly iterating over all elements of the matrices.
3. Input/output errors. Matrices may not be input or output correctly, leading to invalid data.
4. Logical errors. The algorithm to multiply matrices cell-by-cell may contain flaws in how it calculates the results.