What is the significance of both the lack of punctuation and line breaks in the poem?
This is one of those questions that I suspect could have several different answers, depending on how fancy you want to get. I am going to aim at the one in the middle...the one that is easiest to understand and is likely the most common.
Whenever a poet purposefully leaves out punctuation (or puts it in, for that matter,) there is a reason. In this case, it would seem that Williams does not want the reader to pause as much as he/she would if commas or periods were involved. The poem is meant to be read without any chop and on the same breath. It is one full thought in itself.
Well, Mr. Smartypants (you might say to me,) if Williams doesn't want you pausing then why does he have line breaks? Why not just run everything together? That's a good question. First, I suspect that it is because a line break is more of a visual pause than a literal one. That sounds like a crazy kind of answer, but it's not. A period or comma represents either a series of ideas or a total stop. It is a "hard" pause. The blank line, while giving space to the reader, might force a tiny slowdown as the eyes move but it does not do so formally.
There is, of course, also the fact that the blank lines make the individual stanzas look like little wheelbarrows : )
In addition to the answer above, the line breaks are meant to be visual. I have heard this explained this way: Someone who is reading the poem may be visualizing the picture described as they read each line. As each new line is read a new piece of the picture is added to the readers mind until by the end of the line, the whole picture has been put together. The breaks elongate the sentence into distinctive pieces that each fit together to create the entire visual picture.