If you get an unspecified error when backing up your iOS device, there are a myriad of potential solutions (anything from looking for phantom apps on your iPhone/iPad to ignoring a local computer backup and going for an iCloud backup instead). Apple also has an official guide for things to try.
For the one user I saw experiencing this problem, none of those solutions helped. One simple thing did, though—using a different USB port on the laptop. The other USB port seemed to work fine for just about everything else, just not backing up the iPad to the computer via iTunes.