Cleric, technically that timeline is a very weak one indeed. Mostly because I could easily challenge EVERY event mentioned.
1945-USSR drops a-bomb on Berlin ending ww2
How did USSR get the bomb? Why drop it? It is a VERY unStalinesque move.
1969-Britain joins communist block,the last european country to do so.
Um, why? And besides, just HOW do you imagine Communism in Vatican, a perfectly European nation?

Anyway, even if the rest of Europe somehow allies with the Soviets (well, if SCANDINAVIAN NATIONS join this as well I will probably fall over and die), Britain is very unlikely to do so.
1982-Despite US protest mid range nukes are placed on Cuba.
Why so late? And why place them in the first place if the Cold War is pretty much won?
1997-Communist party wins election in Mexico,cheating suspected.
Okay, so maybe Mexico could be a good place to install Communism, or pretty much any other government. But one'd expect USA to act...
2001-USSR invades Americaa and wins,but freedom fighters all around America are fighting the Red Army.
To get that, you probably need Chikatilenko in charge of USSR. Nobody apart from that sociopath is not very likely to even WANT to invade USA, and only he would actually try to carry it out. The Soviets, much unlike what some believed, carred little for "world conquest" in the first place (maybe "world dominance" under "Koba"), and triple so after WWII. The most anti-USA Soviet politicians wanted to simply grab away USA's allies one by one, and let USA's system collapse on itself. In a scenario such as this, with USA losing all of its European allies and markets, that is not too unlikely.
Perhaps this is the scenario that you need for a Soviet Europe. In 1940, Battle of Britain is less decisive and the German air force is much more intact. As a result, Hitler decides to get rid of the British first and THEN attack the Soviets. As 1941 begun, the bombing resumes, and so "Operation: Sealion" begun soon after. The British are not really taken by surprise, but Mannstein drives to London. After that, the front stalemates as the British employ partisan warfare and so on. A failed British "Winter Counteroffensive" 1941-42 nearly led to the British collapse, if not for the Pearl Harbor and the American entry into the war. American troops restore the lines and hold the German countercounteroffensive just outside of Nottingham.
In Spring 1942, Operation: Storm has begun. Soviet forces attacked the lax and greatly-reduced (to provide for yet another push at Nottingham) German defenses and came near Berlin in the beginning of the war. Axis minor powers in Eastern Europe provided somehow better resistance as more of their forces were still at home, but then again, numerous Axis minor troops were comitted to occupying Yugoslavia. Turkey enters the war as well, citing it as a repayment of the Turkish debt to the Soviets, providing Bulgaria's quick collapse. Romania is a tougher nut to cruck, but the sheer manpower poured in proves enough, though casualties are high due to incompetent command there. After that and Hungary's capitulation, the Germans don't have an oil source. The Soviets were somehow checked at Vienna and Berlin, but manage to "liberate" Prague after another expensive offensive. Hitler tries to rally the people of Europe against the Eastern Hordes, getting rather moderate support as many politicians, including Franco, believe that the Germans are about to collapse.
That is not so. Germans still fight on on both fronts, but eventually are forced to pull back to Dover in the English Front and to withdraw the Afrika Korps to defend Berlin. But as oil runs out, and the Soviets begin to adopt the German armored doctrine and combine it with the superior Soviet tanks, the Soviets eventually break through and seize Berlin. After another costly urban battle, in which the Germans used huge amounts of nerve gas in Vienna, the Soviets encircle Vienna though depleting an entire Front in the initial assaukts (as in Army Corps). The German lines are collapsing, and after a coup, led by Rommel who wanted to sign peace with the Western Allies, fails Hitler becomes very paranoid, much like Stalin, and purges several other generals. Final Solution takes place, but by then several prison camps are in Soviet-held territory.
The Germans still fight on, but soon after, the Americans are fresh from their successes in England and land in Norway and Denmark, opening another "Second Front". French, Italian and Yugoslavian communists rebel and partisans tie down large German forces. By 1944, the Germans retreated under joint Soviet-Allied pressure towards Rhineland. Hitler was captured, but commited suicide. Soon after, communists completely take over in France, Yugoslavia, Italy and Rhineland. The Soviets dominate a large part of Europe after the war, though formally it is not so. In Germany, there are two large French (West Germany) and Soviet (East Germany) occupation zones (both communist) in Germany's mainland, while the coastline is split up by Americans and British (North Germany). Japan fights on until 1946, when the Americans decide that Operation Olympus is failing and dropped the bomb on the Japanese HQ in Sapporo. Korea and Japan are divided North-South, as is China.
The Cold War begins, with the West in a serious disadvantage...