If Bush had won in '88, the Berlin wall still would've fallen in 1989, we would've still taken Noriega out of power in '89 as well. The passage of the ADA in 1990 still would've happened as the Democrats still would've controlled congress that year under Bush. Taxes also still would've been raised in '90 as well (this would've hurt Bush as he pledged not to raise taxes in 1988).
The differences would be that the Democrats would've kept control of the Senate in the 1990 midterms as opposed to losing 7 seats and handing the Senate over to the GOP, and the democratic house majority going into 1991 would be larger than it was with Dukakis as the recession would've hurt him with voters.
As for Iraq, does a Bush administration make it clear to Saddam from the beginning that if he invades Kuwait, the U.S. would not support him and that there'd be consequences if he invaded like Dukakis did? If Bush doesn't, we might've gone to war, Dukakis, to his credit prevented this from happening. As for the Cold War, it might've ended earlier than it did if Bush had won. Dukakis gloated about the wall coming down, and thus crippled the U.S.' diplomatic relationship with Gorbachev. Something tells me Bush would've kept a level head through all of it for the sake of maintaining diplomatic ties with Gorbachev, and this would lead to a smooth reunification of Germany and a dissolution of the USSR sometime around 1991 rather than ending in 1999.
As for 1992, Bush might struggle more than Dukakis did. There's certainly going to be voter fatigue with the GOP after holding the White House for 12 years and I'll bet voters still seeing the economy as stagnant through 1992 would hurt Bush as well. Plus, the Democratic field for 1992 ITTL will be stronger than the GOP field we experienced. You might have Mario Cuomo, Al Gore, Bill Clinton, Dick Gephardt, Paul Tsongas, Jerry Brown, and maybe even Ted Kennedy run against Bush. The only candidate of those I can see Bush defeating in a bad year like '92 is Brown. The rest would probably beat him, heck Dukakis only got re elected and by a razor thin margin, because he somehow managed to run an even better campaign in 1992 than he did in '88 while Bob Dole ran a horrible campaign and kept rambling and raving about "Democrat Recessions: and while the voters were upset that Dukakis didn't turn the economy around right away, they knew he understood how hard the recession was on them and that he at least tried to do something about it, only to be obstructed by a Republican senate. Bush seemed like a guy that would've taken a hands off approach with the economy, making it easy for the Democrats to paint him as out of touch.