Can you tell me the significance for A.R. Ammons using colons in the poem "Pet Panther?" I think it is to mark the end of the sentence, but I don't understand why a new sentence starts in the middle of the line and has that space in between the start of a sentence in the first three stanzas.

The colon is ordinarily used to separate two clauses in a sentence, and usually the second clause will explain, expand upon, or illustrate the first clause. The first clause in the poem is "My attention is a wild animal." The rest of the poem is then comprised of a series of clauses which either explain, expand upon, or illustrate the first clause.
For example, the second clause, "it will if idle / make trouble where there / was no harm," expands upon the behavior of the speaker's "attention" and illustrates one consequence of his attention's wildness.
Every subsequent clause in the poem does likewise, each explaining and illustrating a consequence of the fact that the speaker's attention is "a wild animal." In the second stanza, the speaker says that his attention "will wind itself tight / around the pulse," and in the third stanza, the speaker says that his attention "will / pounce on the stalled riddle." In other words, the speaker's attention, because it is "a wild animal," is dangerous, instinctive, and aggressive. The speaker finds it difficult to control his attention, as one might find it difficult to control a wild, untamed animal.
One reason Ammons writes the poem in one long, sprawling sentence, using lots of colons rather than periods, is to reflect the irrepressible wildness of his attention. The clause he begins the poem with runs in all kinds of different directions for five stanzas, refusing to be contained or confined within a more orthodox sentence structure, until it finally exhausts itself in the twentieth line. This of course reflects the fact that the speaker's attention also refuses to be contained or confined, just as a wild animal would likely refuse to be tamed.