What country? They all faced their own issues. However I will give some of the issues that Brecht dealt with in his works. The first which you have already mentioned is the idea of capitalism and the banks which lead to one of his most famous quotes with the three penny opera. Who is the bigger thief the one who robs the banks or the one that founds it? What Brecht dealt with was the Marxist views of the 1920s. Another that would have lead to large debates in his circle at the time is reflected The Measures taken and that is how far are you willing to go in the name of revolution.

Now I will say something separate to the historical question and give some advice as a drama teacher myself. It would be better to use contemporary political issues rather then the ones Brecht himself would have used. Using contemporary issues will allow the students to understand the point of Brecht much better. Now some of them will be the same for example I would use the Bank quote as a stimulus for a performance.

I think you're bang on the money with the three you've chosen so far, and -- to cut a long story short -- I'd suggest 'liberalism' and 'empire' as the two remaining ones. (The state is also a good choice, but probably everything major is covered already through dictatorship and liberalism.) Of course all of these issues are closely linked together, but I'd suggest that's an inevitable feature of political discourse -- look at how strongly major debates like environmentalism and the ideal structure of a capitalist economy intersect today.

The long story (which probably goes into far more detail than necessary for your purposes):

Dictatorship is in my opinion a very good choice, but it's also interesting in as much as it's usually neglected beyond a very superficial level in popular understandings of political thought. Nowadays I often come across people who tell me they don't understand how anyone could have seriously advocated dictatorship. The theory is, I suppose, that the 'totalitarians' of various brands never explicitly supported 'dictatorship', they merely pretended to be democrats and brought dictatorship in through the back door. This is false to the extent that it presupposes a distinctively liberal dictatorship-democracy dichotomy that simply didn't exist in a lot of early (and later) twentieth century political thought.

So I'm curious as to what angle you're planning to follow with 'dictatorship'. This may already be familiar to you, but in any case I'd particularly advise against taking a simplistic dictatorship vs. democracy approach, because one of the defining characteristics of political discourse in the earlier half of the twentieth century is just how fluid the interaction of those concepts actually was. The idea of a 'democratic dictatorship' certainly did not seem as silly as it might sound today.

The thing with dictatorship is that it was very conspicuously not an especially major intellectual issue in the earliest portion of the twentieth century, by which I mean prior to the First World War. The two things that changed all that were the triumph of communism in Russia in 1917 and the establishment of forms of parliamentarian democracy across most of Europe after the war's end. In the first case, the debate about the shape of communist society in the Marxist movement which had largely fallen away thanks to Bernstein and Kautsky was revived with a vengeance, and the idea of the 'dictatorship of the proletariat' became an issue of pressing importance. So you have a very interesting debate on the meaning of dictatorship of the proletariat between the Bolsheviks who are pressing for a kind of 'Jacobin'-style centralised class authoritarianism and their more parliamentarian intellectual opponents -- personified most obviously by Lenin and Kautsky, with Luxemburg as something of a third party.

As far as the second of these goes, the concern becomes how something as fragile as liberal democracy can maintain itself in the absence of the authoritarian structures that characterised much of continental Europe prior to the war. In 1921 Carl Schmitt published an extremely important work, Dictatorship -- an English edition just came out very recently in 2013 -- which argued that the need for emergency powers was a blindspot of establishment liberal political theory. Schmitt distinguished between what he called commissarial and sovereign ideas of dictatorship. Commissarial dictatorship is dictatorship in the 'true' sense -- a tightly limited series of emergency powers given in times of need and rescinded when they pass. Sovereign dictatorship is where the dictator becomes the sovereign, when emergency powers become unlimited. He made the case that this latter idea of 'sovereign dictatorship' only emerged with and after the 18th-century revolutions, and that democracy and dictatorship go hand in hand for a variety of reasons, the need for permanent 'education' of the people being an obvious one.

In this book, he argued against sovereign dictatorship, though ultimately Schmitt would become a leading political theorist of Nazism in the 1930s.

So that's what I'd recommend looking at with dictatorship -- the debate over 'dictatorship of the proletariat', which was really key in establishing Marxism in the shape it came to be known, and the debate over emergency powers and the idea of a democratic dictatorship.

Since this is no longer the convenient dictatorship-democracy dichotomy I was talking about, that leaves more space to explore liberal democracy as an issue in its own right, especially liberalism as such. In, again, the earliest part of the twentieth century you have a distinctive pluralist theory of the state constructed primarily by a series British liberals and adopted to a large extent in America too. Put simply, this pluralist-liberal theory basically sees the state as one social organisation among many and politics as the interplay of a variety of specific interest groups, which the state to some extent oversees and mediates. At the same time, you also obviously have the older characteristics of liberalism persisting, i.e. an emphasis on economic freedoms and property rights, civil liberties, and so on.

This theory comes under attack from all corners in the early twentieth century, including from a new generation of liberals themselves. The Marxists dislike it because it misses the true character of the state as an instrument of class rule -- simply viewing it as a benevolent neutral body instead -- and overemphasises what they view as oppressive, fake freedoms like property rights. The fascists and many continental conservatives oppose it because it deemphasises the role of the state and of proper politics, what Carl Schmitt famously calls 'the political' (the way in which we ultimately divide between friend and enemy, according to him). It promotes a weakened and ultimately unsustainable form of authority in their view. Finally, the 'embedded liberals', people like John Maynard Keynes, come to see the state as playing an important proactive role in securing more expansively defined, economic ideas of freedom.

So there's a big and hugely important series of debates going on over ideas of liberalism during that time.

As far as the other two go: Capitalism is, I think, relatively obvious, though it may be worth deepening it a little from just being capitalism vs. socialism. War is a good one, though a bit broad: there are lots of things that might fit in here -- futurist and fascist militarism and communist ideas of class war to name two. (Trotsky's Terrorism and Communism is a fun read.)

The fifth obvious one that comes to mind is empire. I have to admit though that this is a little beyond my own specialism, since a large chunk of this is to do with British theories of empire and I research continental stuff in general. However, again you have the obvious categories: liberal ideas of empire, Marxist ideas of empire, conservative ideas, fascist ideas, and so on. You have debates about whether empire is necessary, and debates about the nature of empire itself. For Marxism the obvious places to turn are Lenin's theory of imperialism and Kautsky's idea of ultraimperialism. In continental Europe you still have ideas of social imperialism derived from the later 19th century, i.e. the idea of empire as a tool for satisfying the needs of the lower classes -- arguably taken up in a big way by the Nazis. For liberal theories my suggestion is to have a look at some of Duncan Bell's work on the idea of a British Empire at that time.

For some quick further reading you may interested in checking out the Cambridge History of Political Thought volume on the 20th century or Jan Werner-Müller's recent book Contesting Democracy. Just the table of contents and previews of the chapters on Google Books may give you some helpful pointers.

(Personal bias disclaimer: my research focuses on radical European political thought from the 1880s to the 1960s, so I'm perhaps unfairly partial towards debates that fall outside the terms of the modern, 21st-century liberal democratic mainstream.)