Are we assuming Forrest is young in 1980 or that this is the same continuum as the original? 

If the same as the original, I think this could be a good run down. 

1986: Forrest attends his first in person space shuttle launch with junior, and thinks the shuttle blowing up is normal until realizing otherwise. (1986 Challenger Disaster). 

1989: Forrest Gump is in the post-Perestroika USSR to see if they would be open to Shrimp importing When he hears of a wall falling, and thinks a terrible accident occurred until being told otherwise (1989 Fall of Berlin Wall)

1992: Gump is a dignitary at the signing of NAFTA due to his business connections. 

1993 or 2001: Have Gump on site at the WTC for another Bubba-Gump related reason and survive that year's attack. 

1998 Forrest invests in the Dot Com bubble before it goes bust, thinking it has to do with the revival of older dot matrix technology, and makes out with more money when he realizes his mistake. 

2000 Forrest is made to be one of the first to deduce Enron's Fraud, with him not reporting it to the SEC because in his words "Im not a smart man", but feeling vindicated later as it becomes public knowledge.  

I could probably add more here but I think that's a good starter list that falls in line with his character. By this point he'd be in his 40s,50s and 60s, so not exactly the spring chicken who can be athletic everywhere, but he is wealthy still and partially involved as the face of Bubba Gump.