Some states specifically require that turn signals are solidly attached and tape rightly doesn't cut it. A brief scan of Virginia's requirements makes it look like turn signals are about the only thing that DOESN'T have the requirement of being firmly attached, but I've been specifically told that's the case in Maryland for instance.
Around here a SI is usually a light check and occasionally a brake pad thickness check but they usually get that part wrong. According to the manual they should be doing an operational check of the brakes (either the inspector or the owner ride the bike for this) but that NEVER happens.