To make matters worse:
Sometimes an expression in a select clause will be evaluated before filtering expressions in the where clause.
This means that if we have an expression in the select clause that performs a division, where the right side value is queried from a table and a where clause exists to filter any zero's out, it can still go wrong due to a divide by 0!
In such a case you need to harden your select expression by using a case construct to filter out the 0 values before doing the division. It does not matter what the result of the expression is in such a case, as the where clause will filter out the result afterwards anyway.
I doubt many SQL statements in existence that involve such sensitive expressions (and there are quite a few) are in fact hardened. I say this foremost as nearly all of the time code works just fine without, but then it can suddenly break after years of fine operation as some unseen threshold is reached. The second reason is that it generates complicated hard to maintain code, not to mention that it also works slower.
I also think few wil be aware of how far the freedom of execution order in SQL stretches. Personally I think it goes too far as it results in unreliable code or complicated code and thus is counter productive to the things we all want. At a minimum where clause filtering should always happen before select expressions to provide a simple model that is just as good 99.9% of the time anyway.