I think you might be putting too much faith in a few things. 1. The ability for people to come up with systems and procedures that are perfect or close to perfect given enough time and money. 2. The concept that government agencies don’t care about cost or time constraints.
A major theme running through your OP is that there are no financial considerations/constraints and no bean counters nagging about costs. I’m not sure that’s correct. Government agencies have to run to a budget just like anyone else. There may be less pressure than in a commercial operation but that doesn’t mean there is no pressure. There may also be different pressures that are related to politics. I don’t know what pressures there are and I don’t imagine we would ever know but I can’t imagine they operate under some utopian no pressure environment.
Pilots
You could have the best pilots in the world in Air Force 1 but as long as they are people then they are just as likely to see a blue and black dress as white and gold or vice versa as anyone else. Once you get past a certain level of training and professionalism you are still left with the major problem with pilots which is that they are human and suffer all of the same inherent imperfections as the rest of us. The same goes with anything else to do with flight, the systems, the procedures etc. As long as people are involved then mistakes will have been made. You can’t even fix that by designing fully automatic systems, as the systems themselves are designed by people.
Safety on the ground
You can’t have “no danger” of collisions. You can have less danger, but as with pilots, as long as people are involved in the process mistakes can and will be made.
Aircraft maintenance
See above.
Weather
As much as we like to pretend otherwise, weather is not 100% predictable. No one knows exactly what the weather is like until you fly through it. It can be different for the aeroplane ahead of you and different again for the one behind you. There are no guarantees with weather regardless of how much money you’ve got.
Safety in flights
Again, there’s no such thing as “no danger”. Risks can be minimised but they can’t be eliminated. No controller wants to have a collision on their watch regardless of the aircraft involved and will do anything they can to ensure it doesn’t happen. But again mistakes can and will be made.
What could possibly go wrong?
All the same things that go wrong on other flights. The risk may be smaller (or it may not be), but you can still have mechanical failures on the aircraft, you can still have unforecast weather conditions requiring a midflight change of plans that could result in the aircraft having less fuel on board than was planned for. You can still have simple errors made by the pilots. You can still have time pressure on the pilots that forces them to make poor decisions.
If your question is “just how safe can flying be given unlimited resources?” I think the answer is first that we probably don’t know except that it will never be 100% safe and it could probably be safer than Air Force 1 with the President on board, as I doubt they have a true “no cost spared / no pressure” culture.