When is it incorrect to compute factor scores by summing (or averaging) raw variable scores? I understand that a problem will be inevitable if the variables have different scales of measurement.
My inclination is to think that even if the variables have the same scale of measurement it would be incorrect to simply sum (or to simply average) the raw scores of the variables that are "enough loaded" by the factor, since doing so would weight each variable equally, while in fact the factor loads some of those variables more and some of them less. Is my reasoning correct? 
Are there any other circumstances in which it is incorrect to compute factor scores just by summing (or averaging) the raw scores of the factor's variables?
The factor scores are being computed with a view to them being used as predictors in a subsequent regression analysis.
 A: Here's how I see it.
Technically, you are right. Simply adding the scores (or averaging them) weights them all equally and this may not be the optimal solution.
However, it does have certain advantages: 
1) It is simple. Factor analysis is not.  OK, readers of this list probably understand factor analysis; but what about journal editors, dissertation advisers and the general group that will read whatever you write?
2) It is not subject to objections from choosing the wrong options. Factor analysis is, even if you force a single factor (principal components? Maximum likelihood? What priors? etc). If you allow multiple factors, the complexity goes way up as do the number of choices.
3) It often makes relatively little difference. Sums often correlate very highly with factor scores; in many fields, we have so many other sources of error that this may not matter.
So, if you are developing a scale that you hope will be published and widely used, and you are doing a full development, it makes sense to go for FA. But if it's just a one-off scale that won't be used again, it may not be.
