Is it an error that in general, the order of precedence for implicit multiplication is not well defined? I don't think so.
Order of precedence in general is one of those things like the "I before E except after C" 'rule' in English. Albeit it sounds good, it does not seize the crux of the matter. In other words, the only problem here is that people are told that a rule exists, when it really is not a reliable rule at all.
Parentheses work, and should be used to indicate the order of precedence, unless an order has already been agreed upon. The one taught at school is only a common one, not "the" only one used. Calculators are a perfect example of this.
Personally, I would have emphasized more the fact that the conventions vary – not just US vs. the rest of the Western world. That it is a convention and not really a rule at all. Therefore, it's just one of those things that change from calculator/environment/programming language to the next, and can bite one in the ass if one assumes too much without checking the assumptions first.