While it also would be correct to say that construction was begun...and was completed, we are not offered this option among the answer choices.
Our job is not to look for what we think the correct answer should say but to eliminate the four answer choices that contain errors. A, B, D and E each have a clear error, so C is the correct answer.
即使D把it去掉,也是有问题的,即:construction of the Roman Colosseum, officially known as the FA and begun in A.D 69....
如果officially known 和begun都做分词来起修饰作用,那应该是修饰同一个对象。而实际根据语意是,officially know修饰的Roman Colosseum,begun修饰的是construction,所以我觉得还是有问题的