Readings and interpretations of this poem commonly choose to focus upon the imagery and wordplay - for example, the use of words like "mud-luscious" and the conflated name "eddieandbill". Overall, the imagery appears to be positive, pastoral and innocent, and the wordplay is somewhat juvenile and sensory. This seems to portray an idyllic and pleasant story, however alternative interpretations are possible.
The balloonman fits, or does not fit, into this scene in different ways depending upon the reader's interpretation of the scene, and of the balloonman, in a scale that I largely frame to be on a scale of "harmless" to "sinister". The three descriptive terms that apply to him are progressively stranger and more abstract, and it is largely in these terms that we find our chosen interpretation of him.
The word "lame" compliments the description of the balloonman as being old - he has difficulty walking, or walks with an unusual gait. This may feed into the "goat-footed" description as well - perhaps, to a child, the balloonman's gait appears awkward and inhuman, perhaps more like a goat.
The word "queer", by its literary definition, means odd, unusual, and deviating from the norm. It does not necessarily mean sinister; for example, in Alice in Wonderland, Alice describes Wonderland as being queer. In a more positive interpretation, we might substitute the word "funny", in that the balloonman is unusual in curious and harmless ways.
Being "goat-footed" seems to be the most contentious of the descriptive terms. Is the balloonman literally goat-footed, or is this a simile? Being literally goat-footed doesn't seem to fit with the descriptive manner of the poem (e.g. the mud is not literally luscious), so it seems most likely to be a simile, but what is the intent of this simile? It may be intended to mean the old man is somewhat more spry and lively - goats are known for being playful and sure-footed. It may also call to mind images of the god Pan, or a common faun from mythology, forest spirits with a love of pleasure and revelry, though of sexuality as well. Along these lines, someone is sure to draw a comparison to Satan, commonly depicted as being goat-footed. These last two interpretations lend the balloonman a more sinister purpose, particularly in regard to his whistling to the children; he may in fact be luring them to something dangerous.
On this note, it is worth pointing out that, in the final mention of him, the balloonman is described as "balloonMan", emphasizing the Man, and commonly interpreted to mean that his sexual vitality has been renewed. Cummings had a considerably interest in erotic poetry; it does not necessarily follow that the balloonman's sexuality is actually directed at the children, though this is a possibility. However it seems more likely that the balloonman is serving, again, as a counterpoint to the children, an adult perspective on the powers of spring. He may also be seen, in terms of literary technique, as a means by which to "draw out" the children, to give a purpose to their movement, by which the author can afford to describe and elaborate upon that action.