There's an old series called "Seven Days" that covered a secret NSA project where they essentially have a time travel program that's used to prevent all sorts of disastrous events between 1998 and 2001.
(The period between when the series premiered and it was cancelled. My headcanon is that the NSA shut down the program because funding was needed for the War on Terror and because in some way that I haven't figured out yet, the members of the Backstep Program failed in preventing 9/11)
"But Mitry, you said yourself that the basis of the program was that the NSA sent people through time to undo disasters, how is that supposed to affect world history?"
Oh, let's see, for starters we have...
-The 1947 Roswell UFO incident was real (that's where they got the technology to build the time machine).
-The Tunguska meteorite of 1908 was another similar incident (that's where the Russians got the material for their own time travel program from)
-Both the USSR and the United States invested large amounts of effort and resources in building time travel programs. In both cases they decided to use the same ship design. (This stops being so silly when we consider that the Americans apparently went to the lengths of recruiting at least one member of the original Soviet team when the USSR fell.)
-It is possible that this waste was one of the factors of the fall of the USSR.
In incidents covered by the series, and which had sequels anyway (even if the series didn't cover them), we have:
-A far-right cabal led by the United States military, with access to nuclear weapons, which planned to use nuclear blackmail to force the resignation of the President and thereupon launch nuclear war against China. The conspiracy was dismantled, but without a doubt this would have caused a series of purges in the American military commands to prevent more generals from having these kind of ideas.
-Several months later, another high command, in this case a four-star admiral, has to be removed after trying to force nuclear war on China by usurping command of a destroyer to attack a Chinese submarine. This, coupled with the officers mentioned above, is likely to create a sense of "but what kind of nuts do we have in our military" among political and military leaders in the know. It is also very likely that the Chinese are not at all happy because they have shot down a plane and almost sunk a submarine.
-A Russian nuclear submarine sinks in Alaskan waters. Although the catastrophe of spilling the radioactive material was averted, this will in no way help improve relations between Russia and the US.
-A group of Islamist terrorists managed to hack a communications center to transmit false orders for Northern Watch planes to bomb American bases. This will certainly create panic over the fact that supposedly low-tech terrorists possess such abilities.
-Another terrorist hacks into a laser satellite (yes, this US has satellites with laser cannons) and tries to bomb Islamabad in the process. This got undone, but you can't ignore the fact that the US possesses orbital laser weapons in some way, which suggests that they are much more advanced than we are.
-Also, apparently, this United States also possesses molecular analyzers so precise that they can determine a ship's charge at the molecular level from an orbiting satellite. We can imagine the military uses of that technology. Did I mention that NSA security is at the same time so abysmal that somehow the drug cartels know that a time travel program exists?
-A team of American computer scientists develops an AI. This AI then proceeds to disable ALL nuclear weapons in EVERYONE in the world, before attempting to take over Earth. This was not undone (the solution was to turn off the AI AFTER it did this), so we can expect literally every other world power to be FURIOUS at the United States of America for creating such horror. (Presumably by the following week they had managed to reactivate their nukes, but it is doubtful that this would be easily forgotten...)
-The Russians tried to reactivate their time travel program, but the base and all its contents exploded due to a machine failure. The general in charge of the program had previously tried to assassinate the President of Russia with a nuclear weapon (which failed). So the Russians have the same problem as the Americans (crazy with access to chemical and nuclear weapons and delusions of grandeur).
-On at least one occasion, the Nuclear Football was stolen and used to put ALL of America's nuclear missiles into firing mode. Presumably this preparation for what looks like a massive unprovoked nuclear attack by the United States would have been detected by all the other nuclear powers, who would demand detailed explanations of "what the hell are you doing". Even if the launch was aborted at the last minute (literally) this could have ended in total disaster if some other power decided to launch first. This was NOT undone, so presumably the US President had a horrible time trying to explain to the other nations that no, he hadn't gone crazy, and he wasn't trying to "show strength" to push whatever deal he was doing.
