The phrase "numerous criticisms" is correct and usable in written English.
It is typically used to refer to the large number of negative comments or criticism that have been directed at something or someone. For example, "John's new book has received numerous criticisms from literary critics".
There have been numerous criticisms of public opinion polling.
However, numerous criticisms of the methodology of this study design have been identified.
Also, there have been numerous criticisms of the use of the Taser on people with mental illnesses.
There have been numerous criticisms that the show is darker and colder than its earlier iterations, but I think that's a misunderstanding.
Officials said it was a truncated and severely toned-down version of an earlier draft, which had included numerous criticisms of the A.T.F. and used unusually incendiary language to attack its performance and safety record.
Also, deriving all your information from a single source is always questionable in science, even if it weren't the work of Jung, whose theories were/are very influential and far reaching but largely scientifically untestable and subject to numerous criticisms.
It has gained wide-spread familiarity and acceptance, together with numerous complaints, criticisms and improvements.
The choice of Shorey for this post was a controversial one: never a man to conceal his opinions, he had made numerous strong criticisms of German scholarship and the attitude that produced and pervaded it.
Some critics, such as Stephen Jay Gould suggest that any purported 'cosmic' designer would only produce optimal designs, while there are numerous biological criticisms to demonstrate that such an ideal is manifestly untenable.
Two anonymous reviewers provided numerous constructive criticisms, which helped improve the manuscript.
The CIA marginalized and ignored numerous internal critiques, criticisms, and objections concerning the operation and management of the CIA's Detention and Interrogation Program.
