Neither its pipes nor its theories will hold water. (Para. 15)
Meaning: Neither the pipes nor theories will stand up to inspection because of low quality.
"Hold water" here means "stand up to inspection". For further explanation, please to Background Knowledge No. 3.
Notice that the agreement between the subject and predicate is decided by what follows "nor". For example
Neither his colleagues nor his boss accepts his idea. 他的同事和老板都不接受他的主张。
theory: general laws and methods rather than practice
It's ideal to have one's theory based on practice. 理想的是把理论建立在实践的基础上。
hold water: be effective
I think these official papers will hold water. 我想这些官方文件会有用。
He made suggested quite a few ideas about the managing of the company, but none of them held water. 他就公司的管理问题提了好几个建议，但没一个管用。