The phrase "acknowledge widespread" is correct and usable in written English.
It can be used when referring to the recognition or acceptance of something that is prevalent or common.
Example: "In his speech, he chose to acknowledge widespread concerns about climate change and its impact on future generations."
Alternatives: "recognize common" or "accept prevalent".
In their internal briefings, the Marines acknowledge widespread lawlessness stemming from conflicts among corrupt officials, tribal leaders and drug gangs.
But many conservatives who agree with Mr. Bush and Mr. Rumsfeld's step-by-step approach to modernizing the services also acknowledge widespread disenchantment among conservatives regarding the size of the Pentagon budget.
And it was a relief to hear him candidly acknowledge widespread failures in the vast and vastly expensive intelligence and homeland security system and insist that his administration do better.
MPs are trying to find out why News International took so long to investigate or acknowledge widespread phone-hacking at the News of the World, a defunct Sunday tabloid.
True, Owen unequivocally denounces moral complacency, the refusal to confront or even acknowledge widespread human suffering.
The researchers concluded that one main explanation is that upper management "is concerned that large-scale discipline would implicitly acknowledge widespread wrongdoing and lack of oversight".
He acknowledges widespread rumours at the time that du Pont was gay, but does not connect these to their relationship.
The Mail acknowledged "widespread public support" for the strike, and commented: "Sympathy for the miners is a good cause.
In his opening statement, Mr. Brennan acknowledged "widespread debate" about the administration's counterterrorism operations but strongly defended them, saying the United States remained "at war with Al Qaeda".
An Afghan government panel on Monday acknowledged widespread torture of detainees, after a two-week investigation of a United Nations report citing rampant abuses.
In July, ICE officials acknowledged widespread criticism of the program, and asked all participating law enforcement agencies to sign new agreements that clarified its goals.
