The Kenwood TS-680S HF & 6 M transceiver was released over a decade ago now (circa 1989 - 90) but technically it's still a fine radio and they hold a good secondhand value as well. The following is a list of mods that came from FTP sites or through the Packet system over the years, all appear to work without any problems.  I have no idea as to who the original authors were and I've changed the wording a little as things appeared to have gotten somewhat short handed while bouncing around the system over the years.
 

TS-680S  Extended Transmit Frequency mod

This mod makes the TS-680S useful for 4 wheel drive HF frequencies and the like.

Remove the bottom cover and look around the middle of the main PCB, you should see a diode marked as D-31. Removal of this diode from the circuit board will disable the hardware transmit inhibit on non-amateur bands. This will provide transmitter operation from 1.6 MHz to 33 MHz and 49 MHz to 56 MHz. Note that you should reset the radio by holding down the VFO "A=B" key while switching "POWER" on.

Note: For operation on any Australian Maritime, 4 Wheel drive or flying doctor HF frequencies you will need to contact the Australian Communications Authority for licensing details.
 

TS-680S Squelch modifications - adds squelch to all modes

Parts required

       1:  100 uF 20 v capacitor
       1:  10k ohm 5% 1/4W resistor
       2:  1N914 small signal diodes

Modification notes:

All modifications are to the signal board. Remove the signal board to gain access to the bottom of the board.

        Remove R178 a 100 ohm resistor or cut the fill between R178 and C177, R178 is on
        the bottom of the board. The control voltage to the FM chip is now removed.

        Add jumper with a diode in series between pin 14 of IC6 and the base of Q57.
        The cathode of this diode goes to the base, Q57 is on the bottom of the board.
        This is now the squelch trigger control voltage

        Connect a diode between the 8V line (very near IC6) and pin 4 of IC6. This activates
        the FM chip (IC6) all of the time. Cathode goes to pin 4, anode to the 8 volt line.

       Connect a 10 k ohm resistor between IC6 pin 4 and IC6 pin 14.
       Connect a 100 uF 25 volt capacitor between IC6 pin 14 and ground.
       (This will slow the quick squelch action down a bit).

        Tests have shown (using commercial communications monitor) that
       activating FM chip IC6 does not degrade IF strip performance at all.

I haven't actually tried this on my 680s but I've talked to a couple of owners who have performed the all mode squelch mod and reports are that it works fine.
 

TS-680S  6 Metre (50 MHz) Output Power

Remove the 680's top cover (careful with speaker lead), remove 4 screws holding the PA & LPF Filter unit and swing the assembly over to the left of the radio, you will now have access to the SIGNAL UNIT board. Adjust VR15 (also marked as 50M) trimpot while monitoring indicated output power into a 50 Ohm dummy load, both meter and load should be known as accurate at 50 MHz. Adjustment should also be made while monitoring the ALC level, this will insure that there is still some ALC action. In using this method you should achieve a 6 Metre power output of around 20 Watts. Do not exceed this power level as the Mitsubishi output module is spec rated at 19 to 22 Watts, depending on operating frequency. Testing showed that IMD and spurious products became excessive at power levels beyond 20 Watts.
 

Broadcast Sensitivity Modification for the TS-680S

Between 500 kHz and 1.6 MHz attenuation is added to reduce front-end overload on the Broadcast band. Some BCB DXers find this a HIGHLY undesirable feature. If you want attenuation you can still use the front panel "ATT" switch. The following mod will improve the sensitivity below 1.6 MHz...

        Cut the copper between pin 11 of IC1 and R7 (SIGNAL UNIT, M54581P)
        Cut the PCB track between pin 12 of IC1 and R10

       Add a small signal diode (1N914, 1N4148) between pin 11 of IC1 and R7 (Cathode towards R7)
       Add a small signal diode between pin 12 of IC1 and R7 (Cathode towards R7)

       Trace the PCB track from pin 11 and 12 of IC1 you should find a reasonable place to cut
       these traces (to the left of connector CN5) as well a pad to solder the diodes to.

You should notice quite an improvement in the reception of distant AM broadcast signals but look out for overload from nearby stations when using full sized 80 M / 160 M dipole or vertical type antennas.