Is there a perfect, written in stone, set of critiera for evaluating art? Probably not. Even googling for it comes up with nothing immediate.
Here are the factors I try to remember when creating art and the things that are typically there in pieces that that seem strong and compelling: Please add more or correct me if you disagree. These are gathered from aeons of listening to artists, instructors and books. From what I hear, it's pretty typical to have several throwaways for every piece that works out well. This is why I don't mind putting out some snips here with weaknesses, it's part of the process; hopefully at times, the pieces fall into place for a pleasing painting or drawing.
I think the "best" paintings have:
5 shapes (4-6 shapes, because more than that = chaos)
Structure (an organic "dragon-like" connection of darks or lights, without it = mush)
Contrast/Value range, able to see it across a room (without it = mushy and weak, believe me)
Color, ANY colors, but best if harmonious in hue and chroma (no neon yellow in a natural landscape)
Lines, moving the eyes around, not moving them out (curving and geometric, everywhere I go, I see lines)
Texture, strokes, washes, layers
Mood, expression = personal content, universal recognition
Someone (Jim Antley) once told me, many years ago, that painting is like driving a car. At first you get distracted by each action and have to concentrate on pressing the gas, glancing in the rear-view mirror, using the turn signal, but after some time, you do it all at once, automatically. And so it is with the elements and principles of art.