The phrase "agree that the problem" is correct and usable in written English.
It can be used when discussing a shared understanding or acknowledgment of an issue or concern.
Example: "We all agree that the problem needs to be addressed immediately to avoid further complications."
Alternatives: "concur that the issue" or "acknowledge that the concern".
Most people in the tech world agree that the problem of piracy needs to be addressed.
Hitt, Woolsey, and Reicher all agree that the problem isn't oil, it's coal.
They don't agree on much, but they do agree that the problem is a political one.
Canada and the Chamber of Commerce agree that the problem is not at the federal level.
Hare and McGovern agree that the problem lies with the risk-averse nature of the games industry.
Once society and government agree that the problem presented is a serious one and something must be done about it, we are on the right path.
But all seem to agree that the problems uncovered in the Bronxville property tax roll are significant.
Father Dmitry Sverdlov, who is also a well-known blogger, wrote an online editorial in March 2012 proposing that there "are people in the church … who agree that the problems [Pussy Riot] voiced do exist".
Or maybe both sides could agree that the problems of today's homeless did not afflict Joseph and Mary, and that New York's social programs are not relevant to life in ancient Judea.
But most analysts also agree that the problems of Social Security, which provides old-age benefits, could be addressed with fairly modest fine-tuning to future benefits or to payroll taxes.
Individuals with minor mobility problems only, for example, are likely to recognise the possibility of better health states, yet all might agree that the problems themselves are insufficient to merit assignment to "moderate" or "severe" in the EQ-5D's mobility domain.
