It’s funny trying to explain what exactly is wrong with FO3, because a lot of it sounds goofy. “The Vault Doors are different”, and “They still use caps,” sound like nitpicking. But that’s because it’s missing the context of what those things meant in Fallout 1.
These weren’t just aesthetic choices or (like many FO3 changes) done because they were ‘cool’. These have history and lore behind them, lore that’s an important part of the world and the setting of Fallout. There's a reason the Vaults work the way they do in FO1/2. The history of the cap is tied up with the history of the Hub and the water traders.
It might not matter to most people, but fans of the series notice these things. We love the setting, we love the world and to see these elements reused out of context, devoid of their history, is a source of much complaining.
There are a bunch of other things that FO3 messes up, not directly related to the older games.
In FO2, NCR was already a powerhouse, having set up a Republic it was expanding outwards. It brought with it education and a much higher standard of living. About the same time, the citizens of Vault City had an almost modern lifestyle.
Meanwhile, 36 years later in the nation’s capital, they have yet to master the use of a broom to clear out their own living areas. And the idea of raiding that store a few meters to the south for its resources is apparently a shocking innovation that’s yet to occur to them.
For most of the people living in Fallout 2 the pre-war world, 200 years prior, was ancient history. And for some it was merely a fable or legend.
36 years later in the Capital Wastes they reference the summer catalogues, have an intimate knowledge of social trends and are just getting around to writing a survival guide that’s about 180 years too late.
If only Beth had ditched their dumb “always go forward” rule and make FO3 a prequel to the originals, this wouldn’t have been an issue.
Vault Door is nitpicking. One goes out, the other goes in. There is no 'deep meaning' to the doors closing, just a different aesthetic.
As for the 'Caps are silly' arguements. I consider any and all arguements against 3's use of caps null and void because they don't want to apply any real thought to it. It's been proven that traders come from all over in each game, it's not implausible to believe various traders through time have gone 'Hey, you guys should do what we do back home, we use bottlecaps because they aren't easy to counterfeit.' Granted the Hub's were backed by water where as 3's economy is backed by the belief in the cap (Much like the U.S. Dollar), and they can't switch to U.S. Dollars or a unique coin like 2's because Fallout 2 had a centralized government in the region, D.C. not so much, no one to back a unified 'new' currency.
As for the intimate knowledge of the Pre-War world, don't forget D.C. is just one city, not a large region like Fallout or Fallout 2's maps. It's not to inconceivable for regions like Fallout's core region that people, having to adapt to SoCal's largely desert biome, would adapt a more survivalist nature. D.C. is a Pre-War metropolis, everything is there to re-use.
The problem with Fallout 3, as I must keep saying since no one bloody listens to a word I say, Fallout 3 doesnt 'abuse' lore. It's got a bad habit of using things, but with no explanation WHY it's there.