[A]
Making multiple comparisons with a t-test increases the probability of making a Type I error
[B]
Sir Ronald Fischer would be turning over in his grave; he put all that work into developing ANOVA, and you use multiple t-tests
[C]
Nothing serious, except that making multiple comparisons with a t-test requires more computation than doing a single ANOVA
[D]
Nothing, there is no difference between using an ANOVA and using a t-test