Lead section 

The consensus is that the lead section needs to be shortened (see #Proposed intro) even though I disagree with the others on the degree of shortening. Please stop adding text to the lead section! 

Some text I removed/modified:
"is a state that is composed of the island groups of Taiwan, the Pescadores, Kinmen, and Matsu." > "is a state that currently has jurisdiction over the island groups of Taiwan, the Pescadores, Kinmen, and Matsu." This is inspired by the proposal above. The former adheres to Chenism and is POV. Whether the ROC=Taiwan is subject to debate. I don't see how the latter can be disputed.
"Some people view the current ROC that exists on Taiwan as the continuation of the ROC state that from 1912 to 1949 exercised sovereignty over all of China. Others view the state on Taiwan as existing separately from Republican China." > "From 1912 to 1949 the ROC encompassed all of China." Wikipedia:Avoid weasel words. who are these "some people" and "others"? The sentence is too ambiguous to be useful. Again, I don't see how the latter shorter wording is POV or inaccurate. 
"modern Republic of China" > "existing Republic of China". "existing" is less ambiguous than "modern". when does "modern" begin? It also smacks less against the PRC's version of events.
"warlordism" > "warlordism". why the dewikification? the link is relevant.
removed "which had been reclaimed from Japan in 1945". this is not an article on Japan. space is limited. why does this belong in the lead? This is in the history section.
"the KMT set up what it called a provisional capital in Taipei" > "the KMT declared Taipei the provisional capital". the latter is much shorter. the POV of regarding Taipei a provisional capital is alleviated by using the word "declare". The KMT declared. That is not disputed, even not by the PRC.
"the Communists proclaimed the People's Republic of China and claimed to have succeeded the ROC as China and that the Nationalist government in Taiwan was an illegitimate representative of China." > "the Communists proclaimed the People's Republic of China and claimed to have succeeded the ROC over all of China and that the ROC government in Taiwan was an illegitimate government." The PRC not only disputed the KMT as a representative of China in intl organizations and elsewhere. It disputed the very existence of the ROC and its very legitimacy. The former is misleading and wrong.
Removed "While the tense standoff of the Cold War era has largely subsided". Text formerly here about battles is gone. this clause is no longer necessary
Removed "on both sides of the Taiwan Strait". Redundant. It is contentious everywhere (in the realm of international relations etc). and this is too obvious since these are the two sides in contention.
Removed "and one of the original five Security Council members". removed in the interests of brevity. keep this in the foreign relations section. a mention of the UN membership is enough.
"Most major countries now recognize the PRC as having succeeded the ROC as the representative of China" > "Most countries switched their recognition from the ROC to the PRC in the 1970s" The former is wrong. These countries have established formal relations of the PRC, but merely "acknowledged" the PRC's claims over Taiwan. They have not "recognized" Taiwan as a province of the PRC and conduct de facto relations, treating Taiwan as if it were seperate.
"recognized by 25 countries" > "recognized by 25 states" "states" is more accurate.