Since I keep seeing this and sympathize with both sides, allow me to attempt to bridge the gap.
Here's some ways the writing in FO3 is seen as bad:
-Little Lamplight. A 200 year old society of children...? Who reproduces wtf?
-The status of the Capitol Wasteland given the timeframe makes no sense; the surrounding areas should definitely have foliage and wildlife, the river should have clean water; instead it's as if the bombs just dropped.
-James is a scientist who is attempting to purify water by building a water purifier not at the source of a river, but at the base where it connects with the Chesapeake Bay. Gee James, I wonder why it's not working.
-Evil in this game is stupid evil. You have absolutely zero motivation to help people like Burke or to blow up the Brotherhood in Broken Steel. It feels impossible to actually make an evil character within this game without being a straight-up psychopath.
-Tenpenny Tower's societal structure makes no sense. They pay rent to Tenpenny, live there, STILL have to pay for food and other services, and meanwhile Tenpenny pisses their money away on ammo for "safaris." Every single resident of Tenpenny Tower, from the merchants to the guards to the citizens, has a direct interest in knocking him off. He's getting the lion's share of their cash and he's powerless himself. Why are these people calmly paying him and not worrying about the day they run out of cash? Kill him off and pool all your money together so that you can all sustain the utopia you have for as long as possible; letting him piss away that wealth on ammo is just shortening all of their lives.
-Megaton's backstory. You can load up FO3 right now and hear this from the mouth of the old lady in Megaton that's married to Nathan (the enclave patriot guy). In a nutshell? After the bombs were dropped, there were dust storms. Somehow, the hole in the ground that this undetonated bomb created provided some protection from the dust storms. Yknow what also provides protection from dust storms Megaton? That convenient Super Duper Market down the road that none of you have bothered to enter in over 200 years. But no, they know better than me, so they took shelter around a bomb. Then, raiders popped up. How are they gonna protect themselves from raiders? By walking miles (yes that's a quote) to an old airport, completely dismantling it, and then lugging those giant hunks of metal miles back to Megaton so that they could build walls around their pretty bomb. Did it not occur to anyone to just like....live in the airport? Or walk out of the Capitol Wasteland completely, since it's one of the hardest bombed areas in the post-apocalyptic world? Or as I stated, go to the ****ing super market and live there instead?
The entire story is full-on nonsense. Compare this to other settlements within the Fallout series, which tend to spring up because they somehow offer food, water, or they happen to be positioned right where a bunch of trade routes cross paths. Megaton has no secure water source. We still do not know how Megaton eats. Presumably Megaton trades for all of this, but we've no clue what they trade besides terrible stories and radiation.
-How are the Tenpenny residents rich? I mean, wealthy people implies they've provided a valuable service to the wasteland...and yet the wastes are completely devoid of any evidence of progress. What service was provided? How did they make their money? Did every single one of them loot a bottle cap factory, because lord knows none of them provided the area with food and water or other services. If they provided the services elsewhere, why the HELL would they come to the Capitol Wasteland, which is worse than most? How would they hear about the tower?
-Intercontinental travel. Tenpenny is the first confirmed case of someone traveling from Europe to the USA post-war. Bethesda just invented a thing and then completely failed to understand why that might be a really big deal. Furthermore, the question remains as to why Tenpenny would have the tenacity to travel across the entire breadth of the Atlantic, but upon reaching D.C. - one of the crappiest hell holes in the entire United States - he decided it was too much effort to travel any further. Yeah ok.
There's actually tons more, but that's a small list that hopefully gives insights into why people hate the writing. Much of it makes little to no sense, with "rule of cool" governing how communities are built and why, whereas logic rarely plays a role.
I agree that FO3 doesn't have the worst writing ever; I think Bethesda did the best they could given the circumstances. Yes they copy-pasted plots from FO1 & 2, but had they made no callbacks or references to Fallout, people would've complained the game was too different and felt nothing like Fallout cause it shared no familiar faces. In that sense, I can actually forgive all the retcons that took place involving the factions and super mutants. The writing aside from the retcons and repeat plots though...? It's still pretty bad.