The more automatic these airplanes become the fewer "gotchas" there are. But there are still some left from the old days and a few that have been invented.
Everything here is from the references shown below, with a few comments in an alternate color.
If you are in the IFR or VFR pattern and load any published procedure with an altitude higher than your current cruise altitude, the system might change your FMS cruise altitude without telling you. This could be the reason you can't get approach and landing numbers. To change your cruise altitude to something lower, swipe FPLAN, press the PERF INIT tab, press the Alt/Spd button, and look for Enroute Cruise Alt in the middle column.
Have you wondered about the landing gear handle light being too bright at night? Go to night presets and increase the brightness if you need to. That will be dimmer than using the default day brightness turned down to its lowest setting.
I am told that if you go direct to your destination without having an alternate, it will become difficult to add a runway or approach. I'm not sure why, but the problem doesn't occur if you also have an alternate in the flight plan.
When this first happened to us on February 21, 2020, Gulfstream and Honeywell were unaware the problem existed but many users out there had already seen it and come up with a workaround. As I write this now, exactly one month later, Honeywell says they are starting to wrap their heads around the problem but still have some work to do. In a nutshell, when loading a new flight plan after a subsequent flight, the flight plan will sometimes lock in on 160 knots and a low altitude. The procedure for loading a new flight plan taught in the simulator is to switch Nav databases but that doesn't help.
The altitude appears to be 50' higher than the destination's field elevation. From this point we tried swapping the nav database, re-entering the cruise altitude, and starting over. We eventually just powered down to a dark cockpit and brought it back. That worked.
After struggling with it for a few days several members of the user's group said hitting one of the TO/GA switches will fix the problem. We tried it, and it works. Video: G500 FMS Flight Plan 160 Knot TO/GA Fix.
As best we can tell, right now, the problem only seems to occur after flying an ILS, landing, and downloading or manually entering a new flight plan without first shutting the airplane down completely. We've tried this following an RNAV(GPS) approach and it didn't happen. I am not certain that it happens after every ILS, we are still experimenting. Honeywell has not been able to duplicate this in their simulator but I've seen it at least ten times in our airplane and others have told me the same thing happens to them. The research continues, but at least we have the TO/GA solution. (Please let me know if this doesn't work for you.)
One last note about this: the solution had been out there for months but the experts were not aware of it. If you have any other gotcha solutions, please let me know and I'll do my best to publicize it.
If you’ve ever hit the TO/GA button inadvertently during an approach and wondered how to recover the answer is you cannot if you are in IMC. Unlike other Gulfstreams, TO/GA in the GVII not only sequences the FMS into the missed approach, but it also gets rid of the approach navigation aids and pushes everything in the FMS into the go around mode. Unless you are in VMC or have a long way to go, if one of the pilots hits TO/GA, you are going around.
The fix? Be conscious of how you hold the throttles and I recommend you leave the autothrottles engaged until touchdown. But certainly resist the urge to play with them while in the weather on an approach to minimums!
Use of the Warn Inhibit button is prohibited inflight. I am told the only reason we have it is that the CAS Filtering Logic wasn't done when the airplane was first certified.
Gulfstream GVII-G500 Airplane Flight Manual, Revision 4, August 29, 2019
Gulfstream GVII-G500 Production Aircraft Systems, Revision 3, July 15, 2019
Copyright 2019. Code 7700 LLC. All Rights Reserved.