Should the risk of Type II error associated with a n.s. factor be discussed if this factor significantly interacts with another factor? When computing a 2(A)$\times$2(B)$\times$3(C) ANOVA, I observe that only factor A has a significant main effect. Factors B and C were not significant, yet display a moderate effect size and low power. Yet the factors B and C significantly interact with A and with eath other (A$\times$B, A$\times$C and B$\times$C). 
Question: When it comes to writing up the results, it is relevant to indicate that factors B and C may hide a risk of Type II error (i.e. due to their low power yet moderate effect size)?
I have a sense that this is not appropriate since these factors significantly interact with A.
 A: Discussing potential “type II errors” based on a low observed power in your study is a fundamentally flawed approach. If the test is not significant, it necessarily means that it had low power for the effect size you observed. You already know this from the non-significant test/high p-value. This is the gist of the criticism against “retrospective power”.
The flaws of retrospective power analysis seem to make your question essentially moot. The only thing that could possibly make sense is to conduct power analysis based on independently obtained estimates of plausible or practically significant effect size (e.g. from previous studies, theoretical considerations, published meta-analyses or cost/benefit considerations).
One approach that seems always available is to look at confidence intervals for the effect size/parameter of interest. If the interval is very broad and contains values you would consider practically significant (e.g. differences similar to those observed in previous studies of the same phenomenon), you could argue that the risk of a type II error (or even of a wrong sign in the parameter estimate) was present. If it is very narrow, you would consider that you have stronger evidence that the effect is actually very small.
A few references on this problem:


*

*Baguley, T. (2004). Understanding statistical power in the context of applied research. Applied Ergonomics, 35 (2), 73-80. 

*Hoenig, J.M., & Heisey, D.M. (2001). The abuse of power: The pervasive fallacy of power calculations for data analysis. American Statistician, 55 (1), 19-24. 

*Zumbo, B.D., & Hubley, A.M. (1998). A note on misconceptions concerning prospective and retrospective power. Journal of the Royal Statistical Society Series D: The Statistician, 47 (2), 385-388. 

A: While @Gaël Laurans answer has merit, there is a more fundamental reason why this is not appropriate.  For this answer I will be assuming you ran what has come to be a standard ANOVA (type 3 sums of squares, as is produced by SPSS and SAS by default).
Actually, finding that interaction suggests that you certainly had enough power to detect (differing) effects of A... it is just that you did not find an equal effect of A across levels of B or levels of C.  
Let me explain, ANOVA is not like regression in this context, that is a main effect does not refer to the effect of the variable controlling for the interaction.  Instead, your main effect reflects the size of the effect for that variable averaging over all the levels of all of your other variables.  This results in your main effects being "qualified" by your interactions.  That is, the main effects simply can not be interpreted directly in the context of an statistically significant interaction.  
It is for this reason that in an ANOVA context when there are significant interactions people tend to break down and do simple-effects analyses at each level of the variable that the term that the 'main effect' variable of interest interacts with.  In your specific case the A×B and A×C could indicate that there is an effect of A, but only at certain levels of B or C and/or the direction of the effect of A varies across levels of B or C.  The easiest way to tell what is the case will be to plot your data.  However, as you now know this is the nuanced state of affairs, therefore talking about a global effect of A is pretty senseless.
