Onscreen icon to show when there are Saturday/Sunday items not showing
(1) for those that have these items, it would probably be a blessing to not need to hit 7 days every time (making it a persistent changed setting would also change it for this group), but
(2) for those who don't regularly have Saturday items so it's more of a surprise (so they probably won't have changed the setting out of a desire to keep screen real estate).
The notification could just be a small red exclamation point or something similar on the right side of the screen at the top of the calendar. Hovering would have a small 'tooltip' ("Click to show items on Saturday and/or Sunday that are not currently showing") and Clicking would expand the calendar to show the 7-day view (instead of requiring a user to go and look).
I consider this of importance for one main reason: as this calendar moves into the main position, I believe reliability will be one of the single greatest principles to keeping people happy with it (and helping them to have a good experience!). This is something that though it will affect a small number of people, those affected could be heart-broken by missing a Saturday final project or something similar because they have grown to rely on the calendar (something really good) to help them know everything that they need to complete for school. It's a small subset, but it could be heartbreaking for the wrong person at the wrong time and could really frustrate them that nothing told them that there was an item--possibly a very important one--hiding on Saturday night that caused them to fail a class. We want to help simplify the task management portion of students' lives and this is small, but I think it will smooth out that experience.