I can't distinguish any differences between 1976 and 1979 model years, if any, but here's what I can tell.
1980: Pointy headrests exchanged in favor of "full" version. New steering wheel, chrome dot removed from oil/fuel/temp gauge. Triangle shaped turn signal lenses in instrument clusters exchanged for arrow type. 85 mph speedometer added (or it may have been added in 79). Slight redesign to back seat. New front armrest?
1981: New window switches, new hazard switch, and new ACC. US spec W123s get yellow fog lights. Estate is turbodiesel only in North America and the turbo is an option for some Euro 300TDs.
1982: No changes from above, except 300D is turbocharged only for the North American market, and the 300CD (already a North American only car) is turbocharged.
1983: Larger front dome light with map light added, as well as larger rear dome light. Slight redesign to front seats and rear seats, chrome cowls by windsheild dropped in favor of black cowls on "upper end" models. Change of carpet type to "velour" like. 120mph speedometer added. Chrome dots removed from speedometer and tachometer. Black trim that runs above chrome from A-pillar to C-pillar slightly widened. Seat belt latches redesigned. Addition of some sort of black, "plate" between body and chrome on the c-pillar (where the sunroof drain is). Power mirror available on passenger's side.
1984: Antenna grommet goes from chrome to black. Becker Grand Prix radio gets slight remodeling.
1985: Seat pleats changed. 2.88 rear diff replaces 3.07 rear diff. Last model year for W123s.

That's most of it, I'm probably missing a few items.

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'81 MB 300SD, '82 MB 300D Turbo (sold/RIP), '04 Lincoln Town Car Ultimate

Sooner or later every car falls apart, ours does it later!
-German Narrator in a MB Promotion Film about the then brand new W123.