Yes it can detect errors, but it can't continue to function correctly (read: return the correct data) because it doesn't know which copy of the differing data is damaged because it doesn't have checksums.

Moreover, if it doesn't always read both copies of the data (which it may well not, for performance reasons), then you have the possibility of silently propagating damaged data to all mirrors in the case that damaged data is returned to an application and the application then rewrites said data.

Compare that to a filesystem with checksums, which, in addition to being able to detect such a problem, could also continue to function completely correctly in the face of it.