What are differences between industrial statistics and social science statistics/econometrics that are potential stumbling blocks? Main question up front: what are differences between econometrics/social science statistics that and industrial statistics that people switching between the two should be are of?
I got a PhD in mathematical statistics in December and have a job now that is in a different area of statistics than I studied and cared about for years. I studied econometrics for years but now I work in operations research and use industrial statistics. In particular, most of the studies I see now involve designed experiments; this is almost never the case in econometrics.
As my job is to be a consultant, I feel bad whenever I make wrong claims or bad advice to people who are not experts in what I know, and I think I've now twice made a wrong statement. Regarding whether to drop terms from statistical models with insignificant p-values or whether one should favor including or excluding terms that border on being relevant, I tapped on my econometrics lessons and said: the cost of including an irrelevant term is larger standard errors but the cost of excluding relevant terms is biased parameter estimates, which is worse. This is technically true, but biased parameters are irrelevant in the context of designed experiments. In order for parameters to be biased, regressors need to be correlated with each other; since they cannot be correlated in a designed experiment, omitted variable bias cannot be a problem, or should not be expected to be a problem.
(Aside: I still tend to favor including potentially irrelevant factors, though, and deleting parameters from models based on large p-values or selecting parameters based on aggressive AIC optimization makes me very nervous; I would rather adopt a procedure that accounts for model selection automatically, such as LASSO regression, or use some other basis for deleting parameters other than p-values, such as looking at AIC for hand-selected models or looking at Normal plots, but model selection is still what keeps me up at night.)
This is the second time in the span of a few months I offered incorrect advice (the other time hinged on a misunderstanding of terms) and I want to do what I can to minimize this occurrence. My background in econometrics has revealed itself to be a potential stumbling block (sometimes; other times it can be an advantage) and I would like to see a list of other potential major differences between econometrics or social science statistics and industrial statistics that I should be aware of. What else is something I shouldn't say is true because it's a concern in econometrics since it's not a concern in industrial statistics?

I assume by "industrial" statistics you mean 'applied' statistics, where the theory behind it is not as relevant.  But as the above reply says, all fields of statistics SHOULD be more-or-less the same, although some emphasize different things than others.
My own work is kind of in-between academic, social-science-type of statistics and applied industrial statistics. I do a lot of data exploration (biomedical data) and often end up doing regressions and things in an attempt to both explain and predict outcomes.  My advice is do indeed include variables in your regression models that may not be statistically significant IF they improve model fit (or if taking them out reduces model fit).  Two little diagnostics I make use of (talking about linear regression here) is the R-squared value and the standard error of the regression.  The R-squared shows how much the predictors explain the outcome variable, i.e., how well one accounts for the other. If you keep adding variables into your  model, the R-squared ALWAYS goes up, even if those variables have no real value and don't predict things any better.  The standard error of the regression is the average deviation from the regression line that your outcome variables have; i.e., how "tight" the points are around the line.  Both are often overlooked in regression, and both are very useful.
Some other tips of the trade:

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*Sample size matters a lot; often a result won't be significant NOT because of the effect size, but because of the sample size.  Become familiar with statistical power (to detect a significant result) and use it in your reports as necessary to larger sample sizes in the future and to qualify your results.

*Graph your results.  And intermediate steps.  A picture is worth a thousand words. And that includes getting skilled with graphing in your software.

*Learn new techniques often. There are free and paid forums and statistical learning sites on-line. Use them. As Julia Child said, "learn every time you cook."  And in statistics, you are cooking numbers! Scan the literature and see how others are presenting their results; you'll get good ideas for data presentation at least.

*Keep improving your writing.  The write-up of your results is vital.  People hear what they want to hear sometimes, so learn to phrase things carefully, especially any caveats or assumptions or violations of assumptions about the statistical models you use (which isn't always a deal-breaker).
4a) Publish something once in a while, even if it's just a minor technical finding or example in your field with a colleague as co-author.  It boosts your credibility and is helpful to get your next job. And keep your resume updated at all times.

*Keep it simple.  The simplest solutions (for example in regression) are often the best for practical utility.

*Learn bootstrapping.  I've just become familiar with it and it is intriguing. It may be quite useful for small samples.

*Learn TWO statistical software packages. I don't know what field you're in exactly, but I recommend R and SAS as one of them.  (I'm an SPSS man myself, but I could probably earn literally twice as much money doing the same kind of work if I had learned SAS instead. They don't teach you those lessons in graduate school).

