I don't see any major issues with your design, although I would recommend that you attach the vertical plywood elements to the back plate every so often either by nailing through the back, or with 90 degree clips on the inside. This helps brace the vertical elements from buckling under the weight which would be the biggest concern for failure with this type of design.
You mean to prevent racking?
Yea the left and right shifting always bothers me in this type of build, especially w/ all loose shelves.
Nailing th verticals though the plys isn't very structurally sound.
Brackets are better.
When I built cabinets like this commercially we actually used silicone and some screws/nails. I was told the screws were mostly to hold the panel in place till the silicone cured. Granted these were mostly particle/mdf and melamine coated panels.
Others may agree or disagree but the back should be construction adhesive-d (or siliconed) to all vertical members and some nails/screws.
Trick to not get too long of screws or using nailers not to get some ruining your plywood..
Then again can't think of anything I personally built that probably wasn't probably 5x strength necessary..
One of the reasons anytime I even THINK of building a stand I go right to dimensional lumber EVEN knowing in some cases plywood could be better.
Of course things like wood outside corner strips adds a bit of a more finished look and can be structural as well.