Yepp - “One, Two, Three” is notorious in Hollywood history for being a box office failure because it was overtaken by reality. It was shot before the construction of the Wall, but released afterwards, and was completely outdated by that time because the plot relied on the possibility to travel freely between East and West Berlin.
As for the question: I’m too young to have experienced it myself (I was born in West Germany and was six years old when the Wall fell), but in my knowledge it was possible for West Germans to get to East Germany with some, but not extensive, amount of bureaucratic hassle. You would have to apply for a visa, which you would normally get unless you were on some blacklist of the East German regime, e.g. for being an outspoken critic of them. Restrictions were, for most of the time, tougher for West Berliners, as part of East Germany’s general policy of insisting that West Berlin was not part of West Germany. But in times of détente, even West Berliners could relatively easily get a day visa for a day trip to East Berlin (returning on the same day), or get a visa for a longer stay if they had family on the other side to visit.
What was more of a hassle were the plethora of restrictions that applied to you when you went to East Germany. You were not allowed to bring Western newspapers, for instance. East Germany was constantly short of hard currency, so West Germans were required to exchange a minimum amount of West German marks for East German marks per day, at an official rate that vastly overvalued the East German currency; you could not exchange it back to Western money when you returned, and you could not even take it across the border with you, so the only option you had was either to spend it (but what was there to usefully spend it on?) or give or throw it away. There were also restrictions on the areas where you were allowed to go, and the checkpoints you had to use on your way back.
Precise details varied over time; it was a constant feature of the era of separation of Germany that when tensions between the two regimes rose, East Germany would tighten up the rules, partially also to have bargaining power vis-à-vis the West, which tried to give West Germans relatively easy possibilities to stay in touch with family and friends in the East.