I don't think there really was limited language contact, certainly not anything like the situation between North and South Korea and the consequences this has had upon the evolution of informal language. Much of East Germany could pick up TV broadcasts and radio from the West and in the 1980s there were even moves in places that could not do so directly to place transmission boosters. The quality of native TV in the DDR was for the most part so bad that people would not watch it if they could receive signals from the west.
There was also more or less continuous interaction between parts of the two populations via Berlin, as those in the West could (with certain restrictions), travel to work in the East, even after the construction of the Wall and the limiting of Westward emigration.
The Reformed and Lutheran Churches did not accept the political division of Germany until 1978, when the East German churches split away to form a People's Church, but until then there were close links and clergy from either side were relatively free to travel from one side to the other, though under extremely close and sometimes intrusive monitoring by the Stazi.
I did a tiny bit of primary and secondary research on this as part of my linguistics thesis back in 1989. I was interested in the difference between the use of Du (informal you) and Sie (formal you) between the two halves. The Du was encouraged, almost mandated, in the East since the the government saw it as a way of equalizing people (sort of like calling people 'comrade'). The Du in the West was much rarer, offered only once people had become very friendly with each other.
And that difference did come through in my interviews with people as well in my analysis of East German and West German detective novels.
The (minorly) fascinating part was that there was two kinds of Du in the East, one official and one personal. Like if you addressed a random co-worker you said Du, if you began courting them romantically, you might retreat to Sie, and then progress to a personal Du if things got serious.
I'd suggest asking on /r/linguistics
/u/ROBOTNIXONSHEAD and others are absolutely right -- it would be incorrect to speak of "limited language contact" in the case of East and West Germany, for all the reasons mentioned above.
However, while East Germans did not develop a truly distinct German language, it is worth noting that there were changes in language usage as a result of political developments in the East. Perhaps the most significant change worth noting is the divergence of public and private registers. While differences between language-use in public and private exists across many (all?) languages, authoritarian regimes can exacerbate the differences between these registers, as individuals are compelled to conform to certain standards publicly (in the case of the GDR, ideological standards), while they often find some space to express personal preference and/or dissent privately.
In East Germany, the Socialist Unity Party (Sozialistische Einheitspartei Deutschlands, SED) and the state shaped the public register. The state pursued a much more prescriptivist approach to language than ever existed in the West, made possible through its censorship apparatus and vast intelligence-gathering network. Thus, the definitions of words were specified in the East German version of the all-important Duden dictionary (published in Leipzig) to conform with official party ideology (see "imperialism", for instance, which was defined, in part, as "the highest stage of capitalism" per Lenin) as opposed to more "traditional" definitions in the West German Duden published in Mannheim. Other words, especially those with Nazi or capitalist connotations, were eliminated altogether; see, for instance, gutbürgerlich, meaning "homely" but literally translating to "good bourgeois" (an oxymoron in SED German).
Interestingly, other words were kept in East Germany, while they disappeared from use in the West, or words and phrases retained meanings in the East that were archaic in the West. And words like Akademiker (academic) and Brigadier (brigadier) acquired new meanings in the East; the former referred to members of the East German Academy of Sciences, and the latter to members of a small group of workers. (In the West, an academic was an academic, and a brigadier was a military officer.)
Another important features of the public register in East Germany pertained not so much to vocabulary as grammar; in the East, the use of the genitive was widespread in the public register, whereas in the West it began a gradual decline. So, for instance, when East Germany created an equivalent to the Peace Corps, they called it Brigaden der Freundschaft (Brigades of Friendship). See also Haus der Einheit (House of Unity, headquarters of the SED).
Another quirk of the East German public register was the use of the construction "noch + comparative adjective", which translates to "yet/still more comparative adjective". This represented an attempt in official discourse to avoid criticizing the current state of affairs while still indicating areas of improvement; things could be "better yet" but certainly were not bad (the GDR was, after all, a workers' and peasants' paradise. Or so the SED claimed.)
These and other features of the public register were actually taught to East German officials attending Agitationsschule (propaganda school) and the broader East German public came into contact with it on a daily basis. While they might avoid East German television broadcasts, state and party control of the press meant that the newspapers and other publications that East Germans encountered were all saturated with the public register. Plus, East Germans needed to understand and use the public register themselves in interactions with the state, as all official communications (letters, forms, etc) were written in this vocabulary and grammar, and citizens' successful negotiation of daily life with the state meant meeting at least a minimum standard in their responses (though, given the chance, they often rejected that minimum standard, for example in anonymous comments on surveys, etc.) Success in one's career and especially in school could depend on one's mastery of the public register. See also: What determined whether one would get access to higher education in East Germany?
Privately, of course, a different register dominated, one influenced by West German language-use and by English as well (which was only true to a much lesser extent otherwise in East German language use). While publicly the Berlin Wall was the "antifascist protection barrier", privately it was "the wall".
The West did see important developments separate from the East, of course. Perhaps of greatest significance is the development gender-neutral words and usages that did not develop in the East. In contrast to the East, however, most changes in language in the West were the product of popular usage, i.e. "the market" decided.
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