テレビ局の人たちは専門家が火山を調べているところをビデオに撮っていました。ビデオには白い煙が空に上がっていくところや石が飛んでくるところなどが写っています。
The television crew were recording experts investigating the volcano. On the video (you can see) white smoke rising to the sky and stones flying.
Am I correct that all the instances of ところ in bold could be replaced with こと? If so, what nuance/change of meaning does using ところ bring to these sentences?
They are not interchangeable with こと, while they are interchangeable with 場面 and シーン ("scene").
ところ can refer to one concrete situation or scene.
専門家が火山を調べていることをビデオに撮る and 白い煙が空に上がることを写す are acceptable when you want to present them as a general fact (i.e., "the fact that experts investigate volcanoes"). （宇宙から）地球が球体であることを写真に撮る sounds perfect, but 地球が球体であるところを写真に撮る may sound like the earth is sometimes not spherical.
