[Samsung Galaxy Gear] blazespinnaker:
That helped. I've narrowed it down to these two suspects:

73 KB/s (104764 bytes in 0.132s)
pkg: /data/local/tmp/SAMusicProvider_signed.apk
Failure [INSTALL_FAILED_SHARED_USER_INCOMPATIBLE]

1281 KB/s (158158 bytes in 0.120s)
pkg: /data/local/tmp/SAWeatherProvider_signed.apk
Failure [INSTALL_FAILED_MISSING_SHARED_LIBRARY]

I believe SAWeatherProvider relies on TouchWiz. The shared user issue could probably be fixed easily enough. Not sure these libraries should be failing the connection.

Here's the logcat for the fail scenario after I click the paired device:

D/DeviceListActivity(19516): onItemClick()
D/DeviceListActivity(19516): onItemClick() address : D8:90:E8:A1:D1:8A
I/BluetoothAdapterProperties( 959): Callback:discoveryStateChangeCallback with state:0
W/DeviceListActivity(19516): pairing() address:D8:90:E8:A1:D1:8A device.getBondState():12
V/DD/SABtScan(17509): BluetoothAdapter.ACTION_DISCOVERY_FINISHED
V/BluetoothDiscoveryReceiver(19543): Received: android.bluetooth.adapter.action.DISCOVERY_FINISHED
D/DeviceListActivity(19516): pairing() state BOND_BONDED - mAddress is D8:90:E8:A1:D1:8A
D/DeviceListActivity(19516): onReceive() action:android.bluetooth.adapter.action.DISCOVERY_FINISHED
D/DeviceListActivity(19516): onReceive() ACTION_DISCOVERY_FINISHED count:1
V/SetupWizardConnectActivity(19516): onActivityResult()
V/SetupWizardConnectActivity(19516): onActivityResult() RESULT_OK
W/SetupWizardConnectActivity(19516): connectBTHeadset()[D8:90:E8:A1:D1:8A] mBluetoothHeadset = android.bluetooth.BluetoothHeadset@428f5bb0
W/SetupWizardConnectActivity(19516): mBluetoothHeadset.connect(device)
D/BluetoothHeadset(19516): connect(D8:90:E8:A1:D1:8A)
W/SetupWizardConnectActivity(19516): SetupWizardConnectActivity onResume()
I/BluetoothHeadsetServiceJni( 959): connectHfpNative: sBluetoothHfpInterface: 0x69151868
D/BluetoothAdapterProperties( 959): CONNECTION_STATE_CHANGE: D8:90:E8:A1:D1:8A: 0 -> 1
D/BluetoothAdapterService(1114653040)( 959): Get Bonded Devices being called
D/BluetoothAdapterProperties( 959): getBondedDevices: length=2
W/ (19516): mBTReceiver action = android.bluetooth.headset.profile.action.CONNECTION_STATE_CHANGED
D/SetupWizardConnectActivity(19516): BT HFP_STATE_CHANGED_ICS / state = 1
D/DeviceListActivity(19516): onReceive() action:android.bluetooth.headset.profile.action.CONNECTION_STATE_CHANGED
D/WManagerReceiver(19516): BManagerConnectionReceiver:android.bluetooth.headset.profile.action.CONNECTION_STATE_CHANGED
D/WManagerReceiver(19516): Bluetooth HFP_STATE_CHANGED ++ State : 1
D/BTHeadSetReceiver(19202): Action = android.bluetooth.headset.profile.action.CONNECTION_STATE_CHANGED
D/BTHeadSetReceiver(19202): mBTConn data = 1
D/DeviceListActivity(19516): onReceive() action:android.bluetooth.adapter.action.CONNECTION_STATE_CHANGED
I/ActivityManager( 434): Displayed com.samsung.android.app.watchmanager/.setupwizard.SetupWizardConnectActivity: +10s714ms
D/DeviceListActivity(19516): onStop() mIsResultOk:true
D/DeviceListActivity(19516): onDestroy() mBtAdapter.isDiscovering():false
I/BluetoothAdapterProperties( 959): Callback:discoveryStateChangeCallback with state:0
V/DD/SABtScan(17509): BluetoothAdapter.ACTION_DISCOVERY_FINISHED
V/BluetoothDiscoveryReceiver(19543): Received: android.bluetooth.adapter.action.DISCOVERY_FINISHED
W/bt-btif ( 959): info:x10
D/ ( 959): remote version info [d8:90:e8:a1:d1:8a]: 6, f, 220e
D/btif_config_util( 959): btif_config_save_file(L153): in file name:/data/misc/bluedroid/bt_config.new
W/DD/SABtScan(17509): unknown event received : android.bluetooth.device.action.ACL_CONNECTED
D/CompanionService(10769): bluetoothStateChangeReceiver action = android.bluetooth.device.action.ACL_CONNECTED
D/CompanionService(10769): device GALAXY Gear (D18A) @ [D8:90:E8:A1:D1:8A] BONDED
D/CompanionService(10769): Bluetooth device GALAXY Gear (D18A) @ [D8:90:E8:A1:D1:8A] BONDED has HSP|HFP.
D/CompanionService(10769): Headset device GALAXY Gear (D18A) @ [D8:90:E8:A1:D1:8A] BONDED connected.
D/HeadsetConnector(10769): Successfully invoked the getConnectedDevices method.
W/bt-sdp ( 959): process_service_search_attr_rsp
I/BluetoothHeadsetServiceJni( 959): connection_state_callback
D/BluetoothAdapterProperties( 959): CONNECTION_STATE_CHANGE: D8:90:E8:A1:D1:8A: 1 -> 0
D/BluetoothAdapterService(1114653040)( 959): Get Bonded Devices being called
D/BluetoothAdapterProperties( 959): getBondedDevices: length=2
W/ (19516): mBTReceiver action = android.bluetooth.headset.profile.action.CONNECTION_STATE_CHANGED
D/SetupWizardConnectActivity(19516): BT HFP_STATE_CHANGED_ICS / state = 0
D/SetupWizardConnectActivity(19516): STATE_DISCONNECTED
D/SetupWizardConnectActivity(19516): HFP_STATE_CHANGED_ICS state : 0 device Addr : D8:90:E8:A1:D1:8A device Name : GALAXY Gear (D18A)
D/SetupWizardConnectActivity(19516): BluetoothHeadset.STATE_DISCONNECTED mBtAddress : D8:90:E8:A1:D1:8A
D/SetupWizardConnectActivity(19516): Send message show connection fail