I too have thought that there should be such a journal, and found that Expositiones Mathematicae somehow doesn't stop me thinking that.

I think that if one were founding a new expository journal, then a very important feature that it should have would be that getting an article into the journal should be prestigious. And for that it should be difficult to do.

What makes it difficult to write an expository article? One obvious thing is if the mathematics you are writing about is very hard to understand. Sometimes, writing a good clear expository article involves digging deep into the thought processes of another mathematician who has not taken the trouble to say what they were, or of finding a clever way of presenting something that makes it much clearer where the ideas came from. Writing an expository article of this kind is pretty similar to research, in that it involves solving difficult problems. And one could argue that the value to other mathematicians of a good expository article is usually greater than the value of a good research article. (Perhaps I ought to change that "usually" to "often".)

Other features of a journal that I think would make good sense are that it should be online and open access (with plenty of links to other internet resources such as blogs and wikis), and that writing about one's own work should be forbidden. Also, referees should not necessarily be experts in the area being written about, and should be encouraged to be completely honest if there are parts of the article they do not understand.

The advantage of an online journal is that with no pressure to produce issues on a regular basis one could keep the standard of acceptance very high. Perhaps one could even make it so high that the appearance of a new article would be something of an event. But the main thing is that it should be a significant contribution to a CV, or else the motivation for writing such an article would not be high enough.