Does anyone have advice on where and how far apart to drill holes to make adjustable shelves?
I have used various spacings over the years and have settled on putting the holes 1" apart. Any further apart than that and I always ended up wishing I had put them closer together. Make a template to be sure you get all four sets of holes in exactly the same position relative to one another.
All the back is open except behind the doors.
Can you guys think of anything glaringly bad with my design or have any recommendations?
Putting a back on a plywood cabinet like this is the main structural element that keeps the box from racking. If you put pressure on the cabinet down and slightly sideways, does the box deflect into a parallelogram shape instead of remaining a rectangle? If the cabinet isn't braced enough, an uneven floor can produce this kind of racking, which can make drawers and doors bind (in addition to looking bad). So you may need to reconsider your decision not to have a complete back.
If your electronics are going to live behind the doors, you should give some thought to how you will evacuate the heat from that enclosed space.
The two doors in the middle will have dark smoked glass.
I'm not sure how smoked glass panels will look in a painted-and-distressed cabinet. A distressed painted cabinet says, "Antique." Smoked glass says, "Modern." Wood panels in the doors would be a less controversial design choice. If you're worried about controlling the components behind the doors with an IR remote, use an IR repeater system. Here's an example: