I read about the 18 characteristics of a Buddha, and the last three say he has knowledge of the past, present and future. Do mahayanists believe this means he has complete knowledge of everything in the past, present and future, or does it rather mean he has some specific knowledge of the past, present and future? As in, he knows some things that happened or that he did yesterday or some time in the past, some things that happen or which he does right now, and some things that will happen in the future.
In Mahayana omniscience refers to prajna-paramita, the perfection of wisdom also known as the knowledge of all modes.
This comes from direct realization of Emptiness, and results in Buddha having no position, not leaning on any dharma or sign. Not assuming anything as the absolute point of reference. (There are many ways to talk about this.)
Having no position, Buddha knows all positions and all modes of cognition. Hence, the knowledge of all modes aka omniscience in short.