To make things worse the bug is in the memento mile museum so I can't progress any further :'(

The same situation happened to me :(

I need to go to expedition to increase buzz of some items to achieve second star, but the employee stacked and I cannot progress anymore.

I tried to restart the game or switch between museums, but nothing works.

This has also happened to me in Bungle Wasteland. Very frustrating as it’s stopped me progressing! 

 This has also happened to me. I found a workaround. 

If you can afford to buy a second helicopter, you can select a different expedition with the second helicopter. When you do that, you can pick the person that is stuck, and suddenly they will go off on both missions and come back as if nothing ever happened. 

If you can't afford the second helicopter, or you haven't progressed the story far enough, I'm afraid that won't work, though.

Hopefully this helps.

I have the same problem except that even with two helicopters I am not offered to use it, it is bugged so I can no longer advance in the game

I'm having the same issue. Staff became stuck, i could pick him up and move him around but he wouldnt interact with anything. I then tried to put him on a mission but he wont move and now i cant pick him up or dismiss him. That helipad i used is also stuck and useless.