As much as I would love to go full-speed into humor (CKS Memorial becomes Liberation Square? KMT star on flag replaced by a plum blossom?), I think the question deserves a serious answer.
Demographics are a good place to start. Yes, Taiwan is densely populated, but it is also aging, and the sex ratio more and more skewed toward males. Like Japan and Korea, Taiwan will have to figure out how to support its elderly (unless they conveniently die from SARS) and satisfy its heterosexual young men. Unlike these other countries, Taiwan will find it fairly simple to permit high immigration (from China and Southeast Asia). This is different from the U.S. and European strategies because they can “cherry-pick” the most desirable nationalities for immigration as wives and workers.
Economically, Taiwan is blessed with an educated, hard-working workforce which ought to do well in comparison with other places. (Failing that, they at least have a good climate in case everybody has to grow their own food!) So I have confidence in the “fundamentals.”
One of the consequences of more exchanges with China is that crime, particularly organized crime, will increase and become more brutal. Local gangsters are somewhat inhibited in their actions by the presence of family. Not so immigrant mainland gangs.
More “incurable” contagious diseases will arise, and become politically significant. They will especially impact subtropical and tropical regions, like here. This might actually have unexpected benefits, such as effecting a worldwide population drop.
Oil prices will rise to the point where many things we take for granted (e.g. the costs of shipping and air travel, many manufactured goods) will become several times more expensive. On the bright side, large-scale war will also become unaffordable.
Politically and economically, Taiwan now participates in a kind of multinational empire centered on the United States, and encompassing Europe and East Asia. We have to know what the 2025 equivalent will be. At a guess, I suppose that the U.S. will have imploded due to social and economic problems. The machinery of world trade (like the WTO) will still be around, but now dominated by regional blocs. Most people expect one of these blocs to be Chinese, but I’m going to go farther and call it South Chinese. This would not necessarily bode well for Taiwan, since they are natural competitors.
The Taiwanese / mainland rivalry will blur into other rivalries. On one hand, everybody’s kids will intermarry. On the other hand, more mainlanders augmenting the ones here now will exascerbate matters. And then there are the Southeast Asians, who stand to become a third local population group. English and Mandarin will edge out Taiwanese language, because they are more practical. (Think money.)
Politically, I feel confident in predicting that Taiwan will always be corrupt, but nevertherless run reasonably well. Whether they call the result an “autonomous zone” or a “nation” or whatever won’t be so important in the future as it is now.