How come in the daily six remembrances for the golden calf and amalek it says remember and do not forget. For the other four rememberences it only says remember?
Each of the six events to be remembered is mentioned in the Torah in a way that brings some of the poskim to conclude that there is an obligation to recall that event daily by saying something- thinking about it isn't enough. In the two cases to which you refer, the repetition: "remember, don't forget" is the source. In the others there are other pointers. For example, remembering Miriam by saying something is alluded to by the repetion-"remember, protect yourself from leprosy: (Sifra B'Chukotai; Magen Avraham 60 2).