"Fewer errors means better products" or "Fewer errors mean better products"?

I think you are correct that the grammar can go either way. Personally I think the more logical answer in this case is the first version you list ("fewer errors means better products"). I interpret it as having two understood gerunds, and therefore it can be expanded to:

"Making/having fewer errors means producing better products."

Grammatically, I would go with the second statement. However, both statements are correct. Check this out:

“Fewer errors means better products”

Here you are treating "fewer errors" as a single entity that will then result in better products. Due to that singularity treatment the statement is correct.

"Fewer errors mean better products"

In this statement, you are treating "fewer errors" as separate errors hence inferring plurality. Due to that the statement is also correct.

One little trick that i like to play is try using "these"/"this" in either statement to see which brings out the grammatically correct statement. For instance:

In the case where we have treated "fewer errors" as a singular concept, it will be:

"This fewer errors means better products”

In the case where we have treated "fewer errors" as a plural concept, it will be:

"These fewer errors mean better products"

Going from the above, I believe the latter is a very natural way of saying it, and I would go with it in my statement.

To understand more about subject-verb agreement, here are some helpful resources:

Subject-Verb Agreement

Making Subjects and Verbs Agree