I'd like to know if there is something I can do to close the gap or hide the gap in the blinds. Obviously, I can measure properly and purchase new ones but really trying to avoid that.
I've also thought about curtains, but it's also something I'd like to avoid. Are there any solutions to this?
Here is another photo zoomed out. 
A more complete picture would help, but my approach would be to move the blinds closer together, then fill any exposure that then occurs on the perimeter with something the same shade as either the wall or the blinds. (Or as someone else said, curtains that are always pulled back).
Rant: Blind mount brackets should be slotted, and come with pancake-head screws. There's no way in hell to get the screws exactly where you need them (and I'm meticulous, drill pilot holes, etc). Mine are always near perfect, but the lack of slots makes it much harder than it should be.
I've thought about moving them closer. I can do it without issue - I suppose I can try it out and see how it looks.
You can also add sheer curtains in front of them if light is coming through. I find blinds alone are never enough.