Let me begin by admitting that I knew it wasn't the wisest decision to do this, but I knew I didn't have access to a table saw, or a jointer.  I started this project anyway.  I thought that several painstaking hours would make for decent butt joints.  I think I almost have that.  
I measured, measured again, doublechecked the lines, etc. I did a fair job cutting pieces with a circular saw.  Now, I'm embarrassingly admitting that the cabinets don't look like I want.
I fit them together and test clamped them and they look just fine.  After lots of careful sanding with a block, I will have a passable structure.  But I can't get perfect seams.  The outer edge of the joint doesn't always fit perfectly because of ever so slightly rounded connections.  I feel like making the purely cosmetic hairline blemishes disappear is unlikely.
I know I have a good connection up and down each joint, but because it's not totally perfect, I will be praying a filler will do the trick.  
The pieces fit like clockwork, but being a perfectionist without perfect tools, I'm saddened by my results. 

.  
Any words of wisdom?
Ben