There is a definite safety issue, since the DE-5000 is not well protected against external voltages and pre-charged capacitors. Connecting to a powered circuit is bad.
For film and ceramic capacitors, the Q value is a good test parameter.
NP0/C0G ceramic capacitors and polypropylene or polystyrene film capacitors have typical Q values that may be off-scale for the DE-5000 (not a hazard). If such a capacitor shows a Q value around, say, 100 or so, then it is either a lesser-quality dielectric (e.g., X7R ceramic or polyester/Mylar film), or it is defective.
Similarly, you should see a reasonable Q value on the "lesser" dielectrics.
Q, ESR, and D are just re-calculations of the same measured "minority" component of the capacitor (the majority being the reactance).