I understand that the company expects us to handle work flawlessly.
Literal
Work [object-を] flawlessly handle [nominalizer-こと] [object-を] company [topic-は] demands-being [nominalizer-こと] [topic-は] understand.
そつなくこなす means 'to handle competently without slipping up.' こと appears twice as a nominalizer — once to turn the action into an object of demand, and once to turn the whole expectation into a topic of understanding. The double nominalization is structurally notable.