It would, in all likelihood, be impossible for a large transport category jet to even reach an airspeed of 500 knots at an altitude that low. Drag increases with the square of the airspeed and the transsonic region presents some additional challenges on top of that.
A 767 should have sufficient thrust to accelerate past Vmo at low altitude, but Vmo for a 76- is 360 knots at MSL, a long way away from 500. Even if structural and powerplant failures due to overstress weren't an issue, it's safe to say that a 76- would be drag-limited from reaching anywhere near 500 knots in level flight.
With respect to failure modes, there are structural concerns, skin integrity concerns, powerplant concerns, and Mach tuck, and one or more of these would be encountered long before you had a chance to read 500 on the Airspeed Indicator.
- Bending of the airframe - going sufficiently fast will induce the various aerodynamic structures on the aircraft the generate forces and turning moments in excess of what the structure was designed to handle, leading to plastic deformation (and possibly outright failure if the stresses are sufficiently large)
- Elevator vibrationControl surface flutter - this is probably less of a concern in fly-by-wire and hydraulically-actuated control surfaces than for free control surfaces, but at sufficiently high speeds, air particles will strike the control surfaces with sufficient force to displace them and cause them flutter (ailerons are by far the most susceptible to this and the infamous control column "buzz" is caused by this). Sufficiently aggravated flutter has caused control surface separation in several fatal accidents.
- Skin integrity - sufficient suction over the top of the wings has been known to cause material, rivets, and inspection panels to separate and compromise the surface. Probably less of a concern for a stressed aluminium metal or composite skin than for a canvas skin.
- Mach tuck - the center of pressure moves rearward along the wing chord when the aircraft enters the transsonic regime (the exact speed and characteristics of this shift differ by aircraft) and causes nose-down pitching moments, which may become impossible to overcome. This effect is aggravated in a conventional tailplane arrangement by the generation of standing shockwaves and the subsequent change in airflow separation characteristics.
- Powerplant failure - reaching 500 knots would require the powerplant to generate tremendous amounts of thrust, requiring a much greater displacement of air through the compressors (and turbines) and a much hotter burn in the combustion chamber. The resulting engine rotational speeds and temperatures would ruin the engine for further use, if not cause it experience an outright structural failure. There's a pretty infamous case of an Egyptian MiG-25 overflying the Sinai Peninsula at Mach 3+ (the Foxbat was rated for a maximum of 2.8); the engines were toast afterwards.
Though not necessarily a failure mode, something to watch out for in fast-travelling swept-wing aircraft with large wingspans is the possibility the aerodynamic forces might twist the wingtips to the point where aileron functionality is reversed from normal.
Lastly, the control difficulties at such a high speed would stem more from the fact that the control surfaces (especially ailerons) become much more effective at higher speeds (less displacement is necessary in order to generate the forces necessary). Ordinarily, this might lead to an aircraft that is responsive bordering on twitchy and would require very light control inputs, but the story is a bit more complicated in an aircraft like the 76- due to the role played by the envelope protection software and the hydraulic actuation system.