This should not be a problem. It might be a little more inconvenient to cross the road sometimes, but you won't miss anything you want to see and I can't see it making a huge difference. Some people prefer going northbound, as they like driving away from the cliff edges.
For much of the route, Highway 1 is a two-lane undivided road, and the northbound side is just a few feet from the southbound side. There are plenty of areas to stop in the northbound direction, though not all areas have matching turnouts in the same places on both sides, but if you use reasonable judgement, avoid blind curves, and wait until it is safe to do so, you can cross the road as needed. If safety precludes you from getting to a particular spot, you can always drive ahead and turn your car around where it's safe to do so. Traffic tends to naturally slow (and parking areas increase) at common scenic stopping points, simplifying the process.
For some portions of the route, the road is a divided freeway. Many of these areas are less scenic to begin with, but there will be some way to get where you want to go. I wouldn't worry about missing anything going north.
If you're unfamiliar with the state, it's big, traffic on this route doesn't move all that fast, and it will take longer than you think. Plan your schedule accordingly. Sometimes people think of this trip as something to do in a single day, and while that's not physically impossible, there are inland routes if your goal is speed; you're taking the scenic route for a reason.