On constraint-consistency, covariant operators, gauge-invariance, etc

We look at the covariant techniques and the ideas on constraints and gauge-invariance, which were recently employed in [gr-qc/0702104] to support earlier work by the same authors. That work was criticised in [gr-qc/0503042]. Using very simple and well known examples we show that, when adopted, the methods and views of [gr-qc/0702104] lead to basic-level mathematical problems, with analogous consequences for the physics. We provide a few simple rules that should help to avoid similar problems in the future.