Factual error: When the bridges are blown up, some of the bridges are suspension bridges, but the bridge only fails at the point of the explosion. The main horizontal supports are severed, but large portions of the bridge remain magically aloft. The nature of suspension bridges means the remaining vertical cables and road deck would fail as well, resulting in the loss of the bridge between the two main pillar supports.
Factual error: After Bane takes over Gotham, the Army goes to town to stop him. When the convoy is stopped on the bridge, one of the vehicles shown is an M109 Paladin self propelled howitzer, an artillery cannon. There is no reason the army should bring medium-heavy field artillery to a hostage situation, seeing as everything it can do would involve more collateral damage than could be outweighed by the benefits. Even disregarding this, there's no reason at all to bring it into Gotham across the bridge: An M109 has an effective range of more than 30 kilometres, and a battery of guns would easily have been able to cover all of Gotham city from the other side of the river. Plus a howitzer, or any artillery for that matter, parked on a suspension bridge is pretty much useless as their field of fire would be severely limited.