Leonard Bernstein wrote a really great piece for clarinet and piano, his Sonata for Clarinet and Piano. I believe it was written in 1941-42, and it uses a number of mode mixtures that require attention from the performer.
I apologize for a lack of measure numbers, but three bars after letter K of the first movement, the piano begins arpeggiating an Eb diminished chord which would be a iiio7 in the piece (because it is originally in C major). The next bar, the chord is C Eb G, which is a i chord, a prime example of mode mixture.
At this point in the piece Bernstein is actually beginning to develop some previous thematic material from the Exposition of the piece. Naturally, I would venture to call this the beginning of the Development section of the first movement of this sonata. We all know that the development section in Sonata form is a place to spin off in tangents, intertwine melodies, and mix modes! The performer really needs to be aware of this fact, and really emphasize the different notes (b3, and the Ra in the previous iii07 measure). As a performer it is essential also to convey the similarities of this material, but also make sure to essentially lean on the notes that are different (b3, b6, b7).
As a listener, the existence of mode mixture especially in this development section tends to emphasize the main thematic material in a piece. If a composer presents something early on, and this comes up later as the composer plays around with it a little more, we know that it is the most important theme, material, etc. of the piece. Mode mixture can play a crucial role in emphasizing the important material by (if applied to this material) signifying both similarities and also a desire to develop the music.