Frankly, I don't think the law of large numbers has a huge role in industry. It is helpful to understand the asymptotic justifications of the common procedures, such as maximum likelihood estimates and tests (including the omniimportant GLMs and logistic regression, in particular), the bootstrap, but these are distributional issues rather than probability of hitting a bad sample issues.
Beyond the topics already mentioned (GLM, inference, bootstrap), the most common statistical model is linear regression, so a thorough understanding of the linear model is a must. You may never run ANOVA in your industry life, but if you don't understand it, you should not be called a statistician.
There are different kinds of industries. In pharma, you cannot make a living without randomized trials and logistic regression. In survey statistics, you cannot make a living without Horvitz-Thompson estimator and non-response adjustments. In computer science related statistics, you cannot make a living without statistical learning and data mining. In public policy think tanks (and, increasingly, education statistics), you cannot make a living without causality and treatment effect estimators (which, increasingly, involve randomized trials). In marketing research, you need to have a mix of economics background with psychometric measurement theory (and you can learn neither of them in a typical statistics department offerings). Industrial statistics operates with its own peculiar six sigma paradigms which are but remotely connected to mainstream statistics; a stronger bond can be found in design of experiments material. Wall Street material would be financial econometrics, all the way up to stochastic calculus. These are VERY disparate skills, and the term "industry" is even more poorly defined than "academia". I don't think anybody can claim to know more than two or three of the above at the same time.
The top skills, however, that would be universally required in "industry" (whatever that may mean for you) would be time management, project management, and communication with less statistically-savvy clients. So if you want to prepare yourself for industry placement, take classes in business school on these topics.
UPDATE: The original post was written in February 2012; these days (March 2014), you probably should call yourself "a data scientist" rather than "a statistician" to find a hot job in industry... and better learn some Hadoop to follow with that self-proclamation.
Granger causality is essentially usefulness for forecasting: X is said to Granger-cause Y if Y can be better predicted using the histories of both X and Y than it can by using the history of Y alone. GC has very little to do with causality in Pearl's counterfactual sense, which involves comparisons of different states of the world that could have occurred. So Peeps Granger-cause Easter, but they do not cause it. Of course, the two will overlap in a world where there are no potential causes other than X, but that is not a very likely setting and a fundamentally untestable one. Another less restrictive way they can coincide is, if, conditional on the realised history of Y and X, the next realisation of X is independent of the potential outcomes. This point is made in Lechner, M. (2010), "The Relation of Different Concepts of Causality Used in Time Series and
Microeconometrics," Econometric Reviews, 30, 109-127 (WP link), which is written in the potential outcomes framework, rather than Pearl's DAGs.
Addendum:
Let me make an implicit assumption more explicit. The crucial ingredient for my claim is that Easter does not have a fixed date. Suppose you knew nothing about Easter and wanted to forecast its date next year. From historical data (history of Y), you can see that Easter takes place in the spring. But can we do better than that? Using Peeps sales or marketing data (X) from near the holiday, we can see that peeps do Grange-cause it since that data is useful for forecasting Easter more precisely.
The corollary is that Christmas trees sales do not Granger-cause Christmas since if you know that Christmas took place on December 25th for centuries (adjusting for various calendar reforms and church schisms), tree sales do not help.
Best Answer
Strictly speaking, "Granger causality" is not at all about causality. It's about predictive ability/time precedence, you want to check whether one time series is useful to predict another time series---it's suited for claims like "usually A happens before B happens" or "knowing A helps me predict B will happen, but not the other way around" (even after considering all past information about $B$). The choice of this name was very unfortunate, and it's a cause of several misconceptions.
While it's almost uncontroversial that a cause has to precede its effect in time, to draw causal conclusions with time precedence you still need to claim the absence of confounding, among other sources of spurious associations.
Now regarding the Potential Outcomes (Neyman-Rubin) versus Causal Graphs/Structural Equation Modeling (Pearl), I would say this is a false dilemma and you should learn both.
First, it's important to notice that these are not opposite views about causality. As Pearl puts it, there's a hierarchy regarding (causal) inference tasks:
For the first task, you only need to know the joint distribution of observed variables. For the second task, you need to know the joint distribution and the causal structure. For the last task, of counterfactuals, you will further need some information about the functional forms of your structural equation model.
So, when talking about counterfactuals, there's a formal equivalency between both perspectives. The difference is that potential outcomes take counterfactual statements as primitives and in DAGs counterfactuals are seen as derived from the structural equations. However, you might ask, if they are "equivalent", why bother learning both? Because there are differences in terms of "easiness" to express and derive things.
For example, try to express the concept of M-Bias using only potential outcomes --- I've never seen a good one. In fact, my experience so far is that researchers who never studied graphs aren't even aware of it. Also, casting the substantive assumptions of your model in graphical language will make it computationally easier to derive its empirical testable implications and answer questions of identifiability. On the other hand, sometimes people will find it easier to first think directly about the counterfactuals themselves, and combine this with parametric assumptions to answer very specific queries.
There's much more one could say, but the point here is that you should learn how to "speak both languages". For references, you can check out how to get started here.