Prices are determined by the free market. When we say the free market we mean individuals making free choices. The price of a pound of meat is determined by how ever much the consumer is willing to spend and however much the other person is willing to sell it for. The same goes for wages. These prices are determined voluntarily between you and the other person. If either you or the other person does not approve of the deal then you both have the freedom to walk away.
Price floors/ceilings are basically saying there is a justification for having an outside party dictate what prices should be. This is called coercion and is the opposite of voluntary exchange since both parties do not have an equal say in determining value.
edit: As far as problems are concerned, well that depends on the person. From my perspective, I feel its wrong to force others in to situations that can be resolved voluntarily.
From the consumer's perspective, price ceilings are beneficial to most because they get lower prices for goods that are normally more expensive overall. However, the flip side is that the business usually gets less room for profit so they quickly sell out and run out of inventory. Afaik, this is part of the reason why we had gas shortages in the 70's. However, at the same time prices would have sky rocketed if there were no price controls which means consumers would've had to restructure their driving habits while facing higher gas prices although they might've had a better chance of getting gas.
Government intervention through price manipulation may create short term benefits for the consumer (or the business, usually this is never the case), but generally leads to some form of inefficiency because it assumes there is an objective, rational price when prices are actually relative.