I guess I'm fine with Nemo in this range but I'll say that I think The Two Towers rather clearly beats it in the criteria.

Initial Popularity: The Two Towers
Lasting Popularity: Tie
Initial Acclaim: Tie
Lasting Critical Acclaim: The Two Towers
Lasting Audience Acclaim: The Two Towers fairly easily
Influence: The Two Towers fairly easily.

Popularity: The Two Towers slightly
Acclaim: The Two Towers
Influence: The Two Towers fairly easily

Well, do you want me to bump The Two Towers as high as #13 on the 2000s list? Seems excessive to me, I think movies like Gladiator or Brokeback Mountain are more influential and acclaimed as a standalone films. Move Finding Nemo behind it, side by side with Up? Possible but I have my doubts too, does Nemo loses to any movie in the current #17-20 range? You also brought up rating websites' numbers likely lowballing kid oriented movies' popularity in the past. Wouldn't it be a case for Nemo too?

Fair, I guess, but even so, popularity would be a tie or a slight win for Nemo with Two Towers taking acclaim and influence.

Also, I'm really curious how Gladiator is more acclaimed as a standalone film than The Two Towers when Two Towers is ahead on TSPDT, Films101, Rotten Tomatoes, Metacritic, Letterboxd and RateYourMusic, in some cases by a lot.

Gladiator did won Best Picture at Academy Awards but yeah, my bad, it's the popularity which is Gladiator's strongest suite with some influence thrown in.

I could see something like this, maybe
13. Pan's Labyrinth
14. Brokeback Mountain
15. Lord of the Rings: The Two Towers
16. Finding Nemo

Discuss 3.0:

201. In the Heat of the Night - Norman Jewison (1967)
202. Easy Rider - Dennis Hopper (1969)
203. The Crowd - King Vidor (1928)
204. Steamboat Willie - Walt Disney & Ub Iwerks (1928)
205. L'avventura - Michaelangelo Antonioni (1960)
206. Get Out - Jordan Peele (2017)
207. Scarface - Howard Hawks (1932)
208. The Avengers - Joss Whedon (2012)
209. The Battle of Algiers - Gillo Pontecorvo (1966)
210. The Wages of Fear - Henri-Georges Clouzot (1953)
211. Dirty Harry - Don Siegel (1971)
212. Ghostbusters - Ivan Reitman (1984)
213. American Beauty - Sam Mendes (1999)
214. The Asphalt Jungle - John Huston (1950)
215. Network - Sidney Lumet (1976)
216. Breakfast at Tiffany's - Blake Edwards (1961)
217. Pan's Labyrinth - Guillermo del Toro (2006)
218. Cabaret - Bob Fosse (1972)
219. Brief Encounter - David Lean (1945)
220. Out of the Past - Jacques Tourneur (1947)
221. The Public Enemy - William A. Wellman (1931)
222. Airplane! - Jerry Zucker, Jim Abrahams, and David Zucker (1980)
223. Se7en - David Fincher (1995)
224. Brokeback Mountain - Ang Lee (2005)
225. The Lord of the Rings: The Two Towers - Peter Jackson (2002)

I could live with this. It still gives space between WALL-E > FN > Up

I'll take it.

The Two Towers is also very influential, mostly because of Gollum's motion capture and the battle of Helm's Deep.

Not to once again continue down this rabbit hole, but this is another issue I have with Avengers being so high:

Avengers vs. LOTR: The Two Towers:

Initial acclaim: LOTR by a good margin
Initial popularity: Avengers, but with inflation might be a little closer (both highest grossing movie of their respective years)
Lasting Popularity: essentially a tie (LOTR has more votes on IMDB, Avengers has more on Letterboxd, RT the same)
Lasting Critical Acclaim: LOTR by far
Lasting Audience Acclaim: LOTR easy

So it really comes down to influence - LOTR has a very clear win in acclaim, popularity is close with maybe an advantage to Avengers. So unless Avengers is wildly more influential than Two Towers (which we have already established has some influence for sure), I'm not sure if I can see it that far ahead.

We could do
13. Two Towers
14. Pan's Labyrinth
15. Brokeback Mountain
16. Finding Nemo

Do we need to? Nobody here had the Two Towers in their original #201-225 draft and I am afraid we are starting to miss a forrest for the trees. As we mentioned earlier, it was by and large the trilogy as a whole that was influential, Two Towers-specific influence seems more like tidbits to me. The Avengers 2012 seems way more of a catalyst of a franchise superhero movie explosion (Was it alone? No, of course) rather than Two Towers was for fantasy 2000s trends which is somewhat overshadowed by Fellowship and The Return of the King.

Could we remove both Two Towers and Avengers and save them for the next crop? I'm also not saying Two Towers beats it, just might make sense to have them closer together with such similar credentials.

I think the last compromise Tim posted works.