Typical 124 problems are:
Bad flex disk at tranny -- makes a thump when it shifts, vibrates some. Easy fix.
Broken door stops -- noisy or don't work. Easy fix ($18 each!)
Oil leak at front cover (easy fix), oil leak at head gasket front and rear at oil gallery plug -- usually requires new head gasket.
Wiper gets sticky -- if you lube it before it gets too bad, no big deal, but will eventually break the drive gears or burn out the motor.
Rear autolevel suspension can die, either by loosing nitrogen in the accumulators (hard to VERY hard ride), or pump problems (sags) or bad struts (sags). Only the pump is expensive.
If the car has really had good mainenance, I wouldn't expect much else. If not, you will probably need a valve job soon (mine got one at 160,000 miles). Tranny will be OK unless abused or allowed to run low on fluid from leaks (servo o-ring or pan gasket, both easy fixes).
AC may be bad -- not usualy, but possible. Pushbutton control unit usually goes first -- buttons won't stay down or heat won't shut off. Easy fix, not too expensive.
Cruise control may be dead, easy fix but expensive.
You can test the transmission by watching the tach at highway speeds on hills -- if there is a large increase in rpm under load without a speed increase, it is slipping. Shift timing and feel are controlled by a Bowden cable and vaccuum system, so if it shifts funny, look for tired vaccuum lines.
The TE has low rear end gears -- gets lousy milage (21-24 on the highway) and runs about 3200 rpm at 70 mph, higher than usual. Else VERY nice.
Probably needs a tuneup -- plugs, wires, cap, rotor; not too bad, but not cheap. Rough idle problems are common -- most aren't too bad to fix. See other posts.
1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!