The problem here is not the state of registry, or whether or not the operator had an AOC, and nor is it any confusion with the automated features of the Gulfstream.
The problem here is that throwing 2 pilots into an aircraft does not create a crew. Unless the efforts of individual members are co-ordinated and each understands their role, there is no team.
When an F/O believes that 2 minutes after liftoff they are 35 miles from their departure point (a required ground speed of 1050 knots), it shows a lack of SA. When a Captain fails to pick up on this, it shows a disaster in the making.
When a crew member selects an approach for the wrong airport, it shows that he/she is struggling under pressure. When the FMS entry was either not checked by the other crew member, or verified as correct by the other crew member, it demonstrates that this is not a "team" but 2 pilots who might as well each be on different planets.
When a mode selection does not achieve the required outcome (as occurred with the false LLZ capture), it shows a lack of cockpit discipline.
When an abnormal situation occurs, there is usually a task division between crew members, with one pilot flying and communicating, whilst the other addresses the problem. None of that here.
In any non-normal situation, terrain awareness and tracking must be addressed as a priority. No hint of that here.
The fact that an alert controller in an adjacent sector noticed this aircraft in an unsafe environment speaks volumes. Had he perhaps configured his display differently, or "assumed" that the aircraft was in VMC, the outcome would have been dramatically different.
The hinted (by AAIB) post-flight actions of a crew member (implied sabotage of an engine) suggest that something very sinister was going on here, and it had absolutely nothing to do with the comparatively minor inconvenience of a damaged windscreen.