The attached set of tables may give you a start. Your question is ill defined in that it does not cover what kind of sheet metal you are asking about.
B.E.
I am interested in machinery and appliance enclosures, shrouds, etc. We are attempting to come up with a spec for our quality department to use to judge the quality of finished sheet metal cabinet parts from our supplier.
Start by asking your suppliers what specs they are working to.
But in general no, for run of the mill sheet product there is no surface finish standard other than just showing 'acceptable workmanship'.
If you are looking for something else there are ASTM standards addressing surface condition of cold rolled products. A506 covers steels and A480 stainless, but they say little about surface condition.
There are specs for automotive and appliance applications that are very specific, but those are often proprietary specs.
Unfortunately, our supplier looks at us with a blank stare when we ask about their quality specs. We had something similar to "Acceptable Workmanship" as a requirement, but there's a definite difference of opinion between our QC guys opinion of what that is and everyone else's. So we need to put down on paper what acceptable workmanship looks like so we can give it to both our supplier and our QC department.
Rmore:
Maybe you need a new supplier if they don’t have a reasonable QC dept. or set of stds. Have your QC dept. pick a bunch of boxes, and the like, which you have been getting, and really go over them with a fine-toothed comb, for any problems. List these and see if they don’t fit into a number of similar type problem groups. Then, define those issues and your limits of acceptability. That groupings list might include nice tight fitted joints and corners, square, not buckled all over the place, etc.; waterproof or not; no sharp edges so people can’t be cut on them every time they work on the box; properly located and sized internal bracketry and mounting surfaces, and stiffeners on large flat surfaces; limits on size and depth of spot welding markings. Everything you’ve had trouble with over the years on these types of boxes starts out on the basic listing. Is that problem your fault or theirs? All of these things need finer, measurable definitions which anyone can see and measure, without too much arguement. As for sharp edges cutting people, you get to drag their fingers along and over the edges for proof of satisfactory quality. Some Tech. Ed. Sheet Metal text books probably have a QC chapter which might be worth your reading. I suspect that some of the electrical component manufacturer’s groups have some basic stds. lists and limits.