When building cabinets, I make sure the carcass, is small enough to fit, doesn't need to be tight. The faceframe, the part you really see, can then be made to fit perfect.
Working with wood, is all about practice, tricks, and jigs. The tools mean very little if you know some tricks. Although the blades should be sharp.
Your cuts look great, considering you are showing grain, butt joints would have looked silly.
Butt Joint guy, you can do them with hard wood and stain, end grain usually soaks more stain, so heres a trick sand end grain with paper 2x as fine as other areas. This should help match the soak.