Is it safe to eat mouldy bread, even after cutting away the moulded parts? And how can you tell if the mould is harmless or toxic?
In short, the answer is no, it is NOT safe.
Molds produce a range of toxins with a variety of harmful effects, from mild nausea and diarrhea to mind alteration (ergot). This paper claims that mycotoxins can be cumulative, which means that if you eat N loaves of moldy bread within, say, 1 month, it is almost as dangerous as if you eat them in one go.
As ceejayoz has noted, visible mold is merely the «fruit bodies» part which appears only when the bread substrate has been infected at sufficient depth (much like you only get surface mushrooms with caps only when there is enough mycelium mass underground to switch to the spreading phase).
This website states that mycotoxins are very heat-stable, which means that you cannot use moldy bread for croutons, French toast, or even re-baked rusks, as mold poison is unlikely to thermally decompose during cooking.
So this sort of bad food is only suited for a garbage bag due to poisoning potential and unsalveagebility. It is preferable to wrap it in a paper bag or something similar beforehand to prevent further spreading of airborne spores.