Creative embroidery technique to fix a damaged knitted sleeve
I know this is not an embroidery solution per se, but what about binding the edges of the sleeve with something like a light weight felt (use real wool felt, not the kind you played with as a kid), and sewing the binding in place using a saddle stitch? 

If you are concerned about losing the elasticity in the cuffs, you could also use knit bias tape, which should allow you to retain some of the stretch.  

I am still hunting for a picture that shows something similar to what I am imagining. If I find one, I will add it.

In the meantime, hunting for photos led to another possibility when I stumbled on this picture:



Obviously that is a lot more embroidery than you are talking about--but what if you did some sort of embroidered embellishment around the sleeve edges to disguise the uneven edges?  

Before starting either of these options, I suggest sewing a line of stay stitching about 1/2 inch from the cuff edges to help prevent additional raveling.  If you have access to a sewing machine, I would use that, as it will be more consistent, but you could also use a line of running stitches done by hand to accomplish the same thing. 

ETA:  Still no pictures of a bound sleeve, but here is another idea.  What about using a beaded blanket stitch, something like this:

 

The beads will be irregular anyway, so the unevenness of the edge should be much less noticeable. I would use larger beads and a heavier thread/embroidery floss.   

Still not able to find a picture of exactly what I am talking about, but I did find a picture of a similar type of treatment that could also work.  This woman was sewing a boiled wool jacket (you can find her blog entry here), and wanted to add some embellishment to the sleeve cuffs.  So, she cut a strip of fabric the correct length to go around the cuff and used decorative stitches to topstitch the new fabric to the outside of the jacket cuff. Because boiled wool/felt won't ravel, you don't have to worry about the edges of this additional piece.  You could do something similar with your sweater cuffs-creating an outer cuff of felt and attaching that to the outside of your sweater cuffs to hid the raveled edges.