Though an efficient and working economic theory, Keynesianism faces several critiques of various parts of its overall policy. These criticisms stem from various economics schools and pick apart the theory, some of which are actually substantial claims while others seem to have failed the test of time.
The Monetarist School embraced the macro-measurements and treatment of the economy as having a supply and demand equilibrium. However, they argued that inflation was solely due to variations in the money supply, rather than being a consequence of aggrgate demand. Monetarists also believed that the policy of government investment into the people would cause a "crowding out" of businesses because of their inability to compete with the government. This is said to hurt or deprive fiscal policy of its positive effects. Both criticisms are correct and have led to revisions and a more balanced monetary policy in the Keynesian theory.
Criticism also comes from a Classical Liberal point of view. It is said the money used to repair damage, such as stimulus, comes at an opportunity cost, the cost and sacrifice related to the second best choice available in terms of best forgone alternative. Government decisions are also able to be just as misguided as private-sector decisions, leading to unintended consequences. Changes to interest rates either increase GDP or the value of currency, but never at the same time. If stimulus money is misspent, this may lead to lower GDP, reduced value of currency, and high inflation. Stagflation, high interest rate and low economic growth, plagued both Jimmy Carter and Barack Obama. This situation is a dilemma for Keynesianism as actions were designed to lower inflation may hurt economic growth and vice versa. Stagflation and/or misspending stimulus can then cause a net-loss to society. Though these criticisms have proven true, the faults seem to fall not to the theory but the misguidance and bad decisions of people themselves.
The Lucas Critique, which formed the basis of the New Classical Macroeconomics school of thought, focuses on how Keynesianism stands up against changes in policy. With some relationships based on aggregated historical data, whenever economic policies changed decisions made from these models would be misleading. Decisions to maintain conditions that provide the outcome most wanted can often cause firms to change policies. With low unemployment attributed to high inflation in the Phillips Curve, monetary authorities could exploit this by keep inflation high. This would lead to firms' inflation forecasts to rise, changing their employment policy. The Lucas Critique calls for macroeconomists to build microeconomic foundations to their models for the economy.
The Austrian School seems to have the most criticisms for the Keynesian theory. Keynesianism is seen to have a fundamentally collective approach, encouraging centralized planning, which leads to malinvestment of capital; this, according to the Austrian school leads to business cycles. Keynes' study of aggregate relations is believed to be wrong because recessions are caused by microeconomic factors. These economists also believe that temporary government fixes become permanent and expand, which stifles the private sector and civil society. Though not lacking in arguments, the Austrian School tends to lack any evidence to support these claims and often disregards empiracal or mathematical data for other theories or its own. This entire school is actually widely ignored by many economists because they ignore facts and often overstate claims.
Several criticisms have changed parts of the Keynesian theory, ultimately, however, it has stood the test of time as one of the most reasonable theories and is often the basis of policies and newer theories today.
tl;dr: Focus on money. People are idiots. Conditions change, theory too general. Stop liking what I don't like.