There's no simple one-to-one correspondence for all characters, but Wikipedia has multiple layers of special cases and exceptions that can cover most situations (including vocabulary differences). That doesn't mean the text always makes sense after transliteration: The article about the Taiwanese township of Shuili mentions that it was originally named 水裡, but then renamed to 水里 in 1966. At least in the Taiwanese Traditional version https://zh.wikipedia.org/zh-tw/%E6%B0%B4%E9%87%8C%E9%84%89 . If you read the Mainland Simplified one ( https://zh.wikipedia.org/zh-cn/%E6%B0%B4%E9%87%8C%E9%84%89 ) both of these names get simplified to 水里.
Taiwanese Mandarin is really not that different from PRC Mandarin. In fact most college-educated mainland speakers can read works written in traditional characters just fine although I'm not sure on the Taiwanese side for simplified characters. In fact I think a substantial proportion (most?) of Chinese Wikipedia readers just don't bother with changing the character set either way and are fine with traditional/simplified character switches throughout the article (that's certainly the way I read it).
No, there is no perfect correspondence between simplified and traditional Chinese. The simplified Chinese collapses important characters such as “after” and “back”, often causing confusion (you can read more here [1]).
[1]: http://pages.ucsd.edu/~dkjordan/chin/SimplifiedCharacters.ht...
"乾" in Simplified refers to only one of the 8 trigrams, as is used in the word "乾坤"
"乾" in Traditional can mean either the above OR the Simplified "干" (dry)
"干" also exists in Traditional but only means "stem" not "dry"
However, GP's point about translating on the fly is possible. You don't need a very advanced algorithm to translate simplified<->traditional almost perfectly. Unless you're translating poetry they can almost always be disambiguated by the nearby characters very well.
Note though that there are lots of actual word differences in mainland Mandarin and Taiwanese Mandarin. It's not difficult for one to read the other and maybe occasionally asking a question or two but it's nice for every human to have materials available in their native dialect and vocabulary. Much like you probably appreciate that your system offers both UK English and US English and doesn't force you to use the "other" one from what you're used to.