How did the goat fit through the bars?

You answered your own question...

"The bars were hardly wide enough to pull an entire goat between them."

...Hardly wide enough, but wide enough they were. He just pulled hardly...

Considering that Pi was a liar, maybe the goat incident never happened.

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I thought it was clear that the tiger pulled so hard that he broke the goat's bones as he pulled it through.

It was also ties to a rope. Goat suddenly leaps to other side of the fence, and the rope disappears. It's obvious what happened. It's a magic trick!!

"Yeah, well, that's just, like, your opinion, man..."

Such a terrible plot hole...

Was just rewatching this for the first time in probably ten years with FootOfDavros Jnr who instantly pointed out the error.

Then it flashed in my mind that I'd noticed this myself the last time I'd watched it and looked up whether there was any reason for it.

Such an odd mistake to see in a finished film...