the biggest disadvantage of advertisement is that under their influences.
后面is （that under their influences）
That 引导的是表语从句吧?那THAT后面接的句子不应该是完整句吗?难道THAT在从句中做什么成分吗?
如果整个句子是这样的呢？the biggest disadvantage of advertisement is that under their influences，some pople may follow the fashion blindly .