Success metrics for 3D prints
The success metrics are entirely up to you, the user of the printed part. For example, the strength of the part under the load it's desgined for will be critical for an end-use part (such as as hook), but doesn't matter at all for a fit or appearance prototype. Conversely, the dimensional accuracy is very important for a fit model prototyping a complex assembly, but might be unimportant for an appearance prototype or for some kinds of end-use parts.

Because there's a wide range of uses for printed parts, there's a wide range of possible metrics. Mostly they depend on the original design, the print options chosen (e.g. infill style), the material chosen, and the capabilities of the printer. Here are a few:


Dimensional accuracy (of the part compared to the design)
Dimensional stability (does the part warp or shrink afterwards)
Total time to print + finish
Material cost of print (build materials and other consumables)
Weight of printed part
Labour of operating the printer and any post-processing
Surface appearance/smoothness (different for horizontal, vertical, angled, and curved surfaces)
Surface friction
Surface hardness (can you scratch it easily)
Colour accuracy (of the part compared to the design, for colour printing processes)
Colour stability (do they fade over time)
Colour resolution (are colour changes sharp or blurred)
Rigidity (different in different axes)
Failure load (different in different axes)
Non-adhesion across small gaps (as in a tolerance test)
Porosity (e.g. if printing a container for liquids or gases)


A big cross-cutting metric is repeatability. If you make the same print again the next day and repeat any of these measurements, how different a result do you get?

There are also some metrics that are more about the material choice than the way it's printed:


Outgassing
Flammability
Toxicity