Example 1, at least, is not necessarily wrong, as it follows an older convention. It is also slightly clearer than example 2, where "dos" could be initially misread as the Spanish word for "two" or the antiquated abbreviation for a computer's operating system. While "do's and don'ts" is a common enough phrase that any initial confusion will be soon dispelled, if you need to pluralize the word "do" in another context, the apostrophe will aid comprehension.
The convention of pluralizing a word used as a word by adding apostrophe-s appears to have been changing over the last fifty or so years. The 1965 Harper's English Grammar says "this form of pluralization is now used decreasingly," but the punctuation guide in 1970's Webster's New World Dictionary still advocates this style. CMOS changed its recommendation on this between the 15th (2003) and 16th (2010) editions.