Illustrator offers 3 types of stroke corner joins: Miter, Round, Bevel (same 3 as Offset Path filter/effect do).

Miter one just extends the edges of a stroke with straight lines and then cuts the pointy portion off according to Miter Limit value. This works in a majority of cases when we need a sharp corner, but when curvy segments meet at an angle... the straight join becomes obvious.

Meanwhile, Ai has Join Tool.
Here, at the left side of the image a result of expanding a stroke, with a straight mitered join is rather obvious.
So I select the point where the straight segments meet, delete it, and then use the Joint Tool to... well, to join them, following the natural Bezier extensions of the segments.

This gives me a better looking smoother join, with no obvious 'ah, that's a thick stroke expanded'. I can use this method when I have a handful of these... but it’s not convenient to treat hundreds of these, expanding your artwork.

Another solution would be to use inside/outside stroke alignment...
But:
1. it still doesn’t work for open paths — http://illustrator.uservoice.com/forums/333657/suggestions/33963553 (100 votes!)
2. it won’t be helpful anyway if sharp connections happen from both sides of a line, both at inside and outside one

So — please introduce the fourth type of a stroke corner join. Make it fall back to just simple Miter if the curvature of the lines doesn’t allow for them to meet properly (or cheat by changing the curvature just a bit).