Next Level

Color Design
This probably falls under the realm of "art direction" -- but it can make your animation look that much more beautiful. I thought the colors used in To Heart look gorgeous. For anime released over here, I suggest taking a look at the use of color in Fatal Fury -- the Motion Picture or Kiki's Delivery Service.

Voice Acting
Anyone who has ever listened to radio dramas knows how much emotion, power and personality can be conveyed solely by the human voice. If your characters will do much speaking, consider investing in good voice actors. Your audience might not remember what all of your shots looked like, but they probably will remember what the characters' voices sounded like.

(Quality voice acting is why many American anime fans prefer to watch anime subtitled instead of English-dubbed, since few English dubs approach the emotional power of the original Japanese soundtrack. For example, see viewers' opinions of both the original and dubbed Birdy the Mighty here).

Anyone who's listened to Beethoven knows music's power to wring emotion from its listener. At its best, it entertains the ear and enhances the emotion of a scene. (On the practical side...a high-quality soundtrack can bring in additional revenue for a studio, which makes a good composer and experienced musicians a sensible investment. In my opinion).

Yoko Kanno is one of my favorite composers. Her stirring score for Escaflowne greatly contributes to that anime's epic feel. She has also scored such works as the jazzy Cowboy Bebop, the haunting first segment of Memories ("Magnetic Rose"), and the bittersweet Macross Plus.

Sound FX
If the director will rely often on sound effects to convey complex actions happening just off-screen, hiring a good Foley artist makes sense to me.

High-quality sound FX also enhance the visuals on the screen. When Van operates Escaflowne for the first time in the second episode of Escaflowne, the viewer hears convincing sounds of steam whistling and gears grinding. When Escaflowne takes its first step, the sense of massive weight is increased by the heavy crashing sound of the foot (the nice detail animation of Hitomi cringing with her hair blown back by the resulting wind doesn't hurt, either).

Face it -- they get more screen time than individual cels. The audience will have plenty of time to pick them apart, so they'd better look good.

From what I remember, the "Stink Bomb" segment of Memories had some of the most detailed backgrounds I have ever seen. As for anime released here, I suggest studying the beautiful backgrounds of the exotic Shamanic Princess or the gorgeous backgrounds of the wonderful Kiki's Delivery Service.