Your shelves will only be as strong as your weakest part, and right now that's your 1x2 front.
If you are really that concerned, double up your frame on the outside edge. Or add or replace with a clear (no knots) 2x4 instead of an additional 1x2. Even a clear 1x4 will be much stronger than a 1x2. Using clear boards are generally stronger than knotty. The tiny knots you currently have probably aren't a problem, but larger ones can seriously compromise structural integrity.
You can also cut a strip of the plywood to face the shelves. the current 1/4" isn't much, but if you glue it on, it'll add quite a bit of rigidity. Simply screwing it on will likely just break the plywood if there's enough weight to actually bend the shelf, since the weight will really only be applied to the plywood at the screws and so the plywood will move at a different rate than the shelf, essentially making it more rigid than the shelf. Getting a small sheet of 1/2" would be much better and you won't lose too much more space to the shelf. This would also be applied with glue and screws. You could clamp it and leave off the screws, leaving the front smooth. Good wood glue is stronger than wood.
As others have said, fully boxing the shelves will help, especially if you glue on the plywood, but even that only helps so much. What you need to consider is what you want your shelves to hold. Is it just a bunch of light Christmas ornaments, is it heavy home theater electronics, what about a mixture of heavy and light sporting gear, or is someone going to end up sitting on it?
I see what looks like an audio receiver sitting on a shelf at the moment, but I'm assuming there's going to be other uses of the shelves, too. I've had receivers that were light at maybe 10lbs and others that felt like they were 50lbs. Also, are there speakers going to be on the shelf? The size and type can cause different issues. Heavy ones can add more weight than the shelf is capable of handling. A subwoofer could cause the shelf or plywood to buzz annoyingly, or it could add vibrational stress that causes it to fail sooner. And a good subwoofer is normally pretty heavy.
There's a lot to think about when building a shelf like this. Even as simple as it seems, you are already seeing the complexity of what it take to figure out what you support with the shelf.
“Any idiot can build a bridge that stands, but it takes an engineer to build a bridge that barely stands.”
Believe me, I'm that idiot in a lot of things, since I just over-build everything. What the above phrase means is that it takes a lot of math, use consideration, experience, and more to figure out how to build something that meets specifications exactly, instead of being overly strong or even fail completely. And yes, adding a 2x4 to the front of your shelf is probably "over engineering" it, but it nearly guarantees your shelf will remain strong "through the ages" as well as for most things you want to put on it.