From "Building the Perfect Beast," "Not Enough Love in the World" was a semi-hit in the spring/summer of '85. Great song, as is "Sunset Grill" (which features background vocals by Patty Smyth (of Scandal) and Martha Davis (of the Motels)).
Here's my list (coming from a more softer pop/AC perspective):
Your Love is King - Sade
Do It for Love, When He Shines - Sheena Easton (recently saw a YouTube video someone put together with the latter song set to photos/footage of Michael Jackson... couldn't keep my eyes dry)
Soul Kiss - Olivia Newton-John
All Right - Christopher Cross
Twilight World - Swing Out Sister
You're Looking Like Love to Me - Peabo Bryson & Roberta Flack
I Could Never Miss You (More Than I Do) - Lulu
Falling in Love (Uh-Oh) - Gloria Estefan & Miami Sound Machine
Change of Heart - Cyndi Lauper (technically a huge hit, as it peaked at #3, but one that never really registered, it seemed, since Cyndi was in the midst of her sophomore slump at that time; and it really was a great song)
Who Will You Run To?, There's the Girl - Heart (both fairly big hits but, as with "Change of Heart," songs that didn't really register in the public consciousness much)
Running Up That Hill - Kate Bush (probably a bit too art-rocky for U.S. Top 40 radio in '85, despite having been a huge hit in Canada and the UK; I still love this song, and it does get some alternative airplay to this day)