iphone 3g bluetooth with garmin 680

I really doubt there's a setting you're missing. You're probably lucky that BT even works at all with the iPhone/680 since the 680 is ~2 years old. Usually, the culprit when BT phones don't work correctly with Garmin devices is the Garmin device. Garmin's BT implementation is not considered very compatible, nor stable with many phones.

For instance, my nuvi 760 pairs and operates just fine with all options working with my Verizon MotoRAZR.

That same exact phone is flaky with my nuvi 765T (voice dial does not work 90% of the time, the phone book does not transfer over 20% of the time) despite the 765T being one year newer than my 760.

nuvi users with BT problems/issues are likely better off just purchasing a cheap BT headset and avoiding the Garmin BT frustration factor.

you can try updating Garmin bluetooth firmware. Use Garmin WebUpdater to search for updates.

You are absolutely right. BT already killed my two 765s. I have Nokia N95 and I always have issues pairing it Nuvi 765. It will re-boot 765 or do some gSP firmware update and then shuts off for ever.
So now I got third replacement unit and not going to try pairing it agian.

I never had any issue pairing my Nuvi 760 with same phone.