95% of Han Unification doesn't seem like a problem to me. The slight stylistic differences between Chinese and Japanese where it's just a matter of "these tiny strokes point slightly left in Chinese and slightly right in Japanese" can still easily be understood no matter what font. Even slightly more stylistic differences don't actually cause any problems. For example, these two Kanji: http://jisho.org/search/%23kan... and other Kanji that have these shapes inside of them. The fonts tend to show the Chinese version: In the first, the top line is the same as the 3rd/4th, but Japanese usually write the top like a tiny dot almost, as seen in the stroke diagram graphic. In the second Kanji (scroll down), the last stroke is vertical in Chinese, but diagonal and connected differently in the Japanese version. Japanese people, in my experience, don't seem to have any problem with these kinds of differences.
Other more major differences caused by Kanji simplification over the years has also resulted in two codepoints in Unicode, so the Chinese and Japanese characters that *historically* had the same drawing, are now actually usable in either language still. For example, https://translate.google.com/?... shows the Japanese and simplified Chinese "fish". Japanese still use 4 dots on the bottom, Chinese use a line. This was given two codepoints and doesn't seem to be a problem. Many other differences were given two codepoints and Chinese fonts typically don't include any definition for the Japanese version and vice-versa.
The example I gave in my original post, about the Kanji meaning "leader" is one that really baffles me. Why was such a major difference in drawing merged into only one codepoint, and why was it never separated out into two codepoints in the next version of Unicode? There are other Kanji with major difference in appearance that share a single codepoint because of Han Unification, and these ones cause a lot of trouble. Japanese people typically don't recognize the Chinese version of "leader" as having any meaning at all. It's just scribbles to them, and when a webpage or document tries to display Japanese text but Windows or whatever decides to fall back to a Chinese font, the entire meaning is lost, because of Unicode.