Strange you should ask.; Other than lost gas milage the only real affect is going to be poorer throttle response.
To my knowledge, here's what's going on;
It's one of those common misunderstandings that a car with alotta power is going to have better throttle response. In all factuallity the the exact opposite is true. Jump in a "Built" motor and it's gonna have the farthest thing from throttle response at lower rpms you've ever seen. If wild enough your gonna have to move the idle up. What's going to happen is the overlap is going to be increased due to the larger duration. What this is going to do is make the motor less efficient at the lower power rev-range and able to breath better at the higher rev-ranges. With out the volume of large throttle openings and higher piston movements(rpm), the motor is actully going to lose pumping efficiency. There fore it will take more movement of your right foot to get the car going, but it will have more power.
As far as the affects on the rods; The rod strenth comes into conceren at rpm and piston weight. I'm sure there's a point where massive cylinder pressure will destroy a rod, as will detonation. But the main reason why a rod breaks is rpm and piston weight or detonation related. If you don't over-rev it, and you don't detonate it, chances are it's not going to break. The bottom end really doesn't know what the top end is doing, unless it pre-ignites, it pretty much only knows how fast it's spinning. In boosting a motor, the cylinder pressures are really high and the motors become more prone to detonation. If just a little lean the explosion becomes really violent and hot. Also with the higher cylinder pressures, poor fuel, poor fuel ratios, and hot spots in the cylinder can also lead to detonation. Usually what you'll see there is a rod bent, or bent till snapped, but what these guys seldom show you is the specked, chipped, and burnt pistons that tell the real tale of that cylinder detonating(you can see this in the rod bearings to). An over-rev is usually a stretched rod bot or a rod pulled apart; fracturing and sending chunks all about.
The cams mentioned earlier(I could look into it further) aren't wild enough to move the peak power out of the factory rev range. There's limits of the intake and exhaust flow capabilities to consider also.
There's also air-speed throught the port that affects pefromance/throttle response, but being we're not talking about porting and different intakes; I don think there's a need to get into that right now.
Snappy throttle; pretty much gone.