Taxpayer-funded college education may be a good idea, but I have yet to hear exactly how he will ensure the education funds are used solely for education, and not merely to - say - install a new building on a campus, or create unnecessary job positions (such as a new manager).
Based on the summary of the College for All Act he introduced in the Senate, that would be prevented the same way that any misuse of federal funds is: The law itself prohibits it.
To qualify for federal funding, states must meet a number of requirements designed to protect students, ensure quality, and reduce ballooning costs. States will need to maintain spending on their higher education systems, on academic instruction, and on need-based financial aid. In addition, colleges and universities must reduce their reliance on low-paid adjunct faculty.
States would be able to use funding to increase academic opportunities for students, hire new faculty, and provide professional development opportunities for professors.
No funding under this program may be used to fund administrator salaries, merit-based financial aid, or the construction of non-academic buildings like stadiums and student centers.
From the full text, Title 1, section 101(a)(1):
the Secretary of Education ... shall award grants, ... to enable the States to eliminate tuition and required fees at public institutions of higher education.
If a state or university misused the money, that would qualify as grant fraud.
Who is responsible for monitoring fraudulent behavior?
Federal Inspectors General (IG) within each government agency have been established as independent and objective units tasked with combating waste, fraud, and abuse in their respective programs. When fraud is suspected, other government entities, such as the Federal Bureau of Investigation and the Financial Fraud Enforcement Task Force, may get involved.
At the very least, the federal government would then not cover the costs of the non-compliant expenses by withholding money.
Even if federal funding to states were not to be considered a grant (and thus not grant fraud), there's going to be equivalent mechanisms in place already - earmarked federal funds are a common thing, so no matter what the mechanism, there's certainly going to be some form of oversight already in place.