The teaching building is said to have been completed by the end of next month. 对不对

by the end of next month明显是将来的，未完成；而have been completed 又是表示已完成，显然自相矛盾，将have been 改为原型即可。
The teaching building is said to be completed by the end of next month.

【原文有误】
注意时间状语 by the end of next month到下个月为止，这是将来时间，因此，改为
The teaching building is said to be completed by the end of next month.
【注意】be said to have done 表明不定式中的动作早于主语动作“据说”。