Making this tonight! Thanks so much, everyone. ;o)
I can't imagine why not. (sounds great!)
I love dill, but I've never really thought so much about its use in Turkish beef and lamb dishes. If you leave it out, you'll just get a flavor shift, away from an almost sour note to some flavors you like more. I assume you're keeping the mint? But really--it's your dinner and the beef and eggplant could lend themselves to a whole lot of non-dill flavors. Parsley would be great.
I do a lot of middle eastern cooking and although I like dill, for this I think parsley and the mint would be an even better match. I'm sure its delicious as intended but in my opinion it would be perfect with the parsley.
I think it will taste different, but good nonetheless. The mint, I think, is the key here.
If you don't like dill don't use it! Use what you love and it all works out. I concur with the opinions above - parsley and mint.