Enzymatic error rate
First it is important to define what actually an error is. What you call misproduct is actually a right product for a different substrate. The enzyme has a low specificity; but you won't say hexokinase is error prone because it has wide substrate specificity. The question is — is specificity critical?

Coming to the example of DNA polymerase, you should note that DNA polymerase only adds a nucleotide to the DNA strand. Here the template DNA strand acts like a co-enzyme and it is the template DNA that provides specificity to the reaction. In this case the specificity is really critical and there are mechanisms that help in ensuring that.

Other enzymes also make errors and the probability of making errors depends on different parameters. Take the example of restriction enzymes that are supposed to cut at a specific site. When this specificity is lost we say that the enzyme is showing a "star activity" i.e. non-specific cleavage. This depends on different parameters such as buffer composition, enzyme concentration etc.

In general specificity is provided because of high affinity of binding towards one molecule compared to the other. These binding reactions are second order — a high affinity substrate will bind to the enzyme even at a low concentration, however if you increase the concentration of the low affinity substrate or the enzyme, then at some point the rate of binding may be significant enough to create a "wrong" product.

Sometimes there are cases where the enzyme can bind to a wrong substrate but cannot create a product. This is the typical case of a competitive inhibitor. It is also possible that a certain molecule is good at binding but the conversion rate is slower.

To conclude, these kinds of "errors" happen with many enzymes but it is very critical in case of DNA polymerization. You can get information on star activity of restriction enzymes (just google it).