No, Dalton Trumbo isn't missing the punctuation keys on his typewriter. While he might not use any words that will send you running to a dictionary, his insistence on mimicking the language of an average Joe (especially when that average Joe can't speak and is confined to thought alone) means that Joe often thinks in sentences that run together or that are only punctuated by exclamations of "O Jesus Christ."
Stream-of-consciousness was a technique associated with the Modernist movement at the beginning of the 20th century. Here's how it works: a writer tries to mimic on the page the way a person thinks and the ways that words and thoughts are associated when a person thinks.
Now, we don't always think in complete sentences, right? Sometimes, we just think in words or sound or images, all pretty loosely connected. Guess what? That's just the way Joe thinks—especially, when he's anxious, which is pretty often. Take a look at this doozy, for example: "He's still got air and he's not struggling and he's got willow trees and he can think and he's not in pain" (5.10).
The thoughts and images all just kind run together (willow trees, anyone?), but we can figure out what's going on, because we've been anxious and had run-on thoughts like that, too.
Sometimes, when Joe is panicky, he'll repeat things over and over again in order to get hold of himself:
He had to stop this. He had to stop things from fading away and then rushing back at him. He had to stop the smotherings and the sinkings and the risings. He had to stop the fear that made him want to yell and holler and laugh and claw himself to death with a pair of hands that were rotting in some hospital dump. (7.1)
"He had to stop" gets repeated over and over, and this shows us that Joe is trying to take control of a situation he has very little control over (and in case you were curious, this kind of repetition at the beginning of a sentence is totally called anaphora).
It's important for Trumbo to make Joe someone we can relate to, and that's one of the reasons he has Joe think in everyday, colloquial language that is believable. Joe's not a scholar, but he's not illiterate, either: he's average, remember? So the language he uses is neither easy nor difficult. Even though the stream-of-consciousness can be hard to follow, the actual language Trumbo uses is fairly easy to follow. We can usually understand Joe even when he's going off into panic land.