Effects of Price Fixing on Labour

Not controversial: price controls are bad.
Minimum wages are price controls on labour. Price controls prevent markets from clearing.

The labour market in particular needs to clear. Labour is literally the only input that every business needs, so labour mispricing affects the entire economy.

Precisely because labour is so critical, the price floor isn't quite as destructive of jobs as it should be. Replacing labour isn't as easy as switching from black pepper to red pepper. However, there's a flip side: in the long term the floor is even more destructive.

When labour supply grows and labour price should fall, the wage-floored economy generally has no spare capacity of inputs it can swap for labour, having already used them up.

Immediately, extra supply a free market could absorb instead goes into unemployment. 
Further, the price of labour does not fall, causing the wage-floor price derangement to propagate all the way up the labour price schedule. All labour is now overpriced, leading to a shortage. More intuitively, the number of jobs bidding for labour drops, causing unemployment across the wage spectrum.

Because there's a shortage of jobs, there's a shortage of wealth creation. Wealth per capita drops, and the price of money drops - we see inflation.

Because poverty is on the rise, politicians promise to fix it by increasing the minimum wage. Because labour is relatively slow to adapt to market conditions, this seems to work for a moment, but in the long term the cycle repeats until we reach full communism except there's no factories, no jobs, and everyone who doesn't physically hold a farm starves to death.