While at first instance the law appears to do good, eventually the economic incentives are such that minimum wage laws does more harm than good. Let's explore the reasons for that.

An employer-employee contract is not a coerced transaction. It happens in an environment where both parties read and understand the terms and conditions to the contract. The employee promises a set of skills, backed by discipline, commitment, education, previous work experience and  many attributes. In lieu, the employer promises to pay wages that commensurate these benefits that the employer receives. For clearer understanding, we need to assume all the disclosure are true and fair - that is the contract is clean in all aspects. The wages set here form the market-determined wage rate.

A mental-model of a contract:

Employee Brings Employer Promises
Skills - A, B, C A commensurate wage: total $$$
Discipline $
Commitment $
Honesty $
Track record $
Age & experience $
Degrees, Certificates, Vocation $
References from prominent people $

A contract of this nature allows total flexibility. Both the sides of the table are completely malleable. You can drop certain rows in the left side of the table and see a corresponding drop in the wage. This isn't how mathematically contracts are structured but this is the economic sense of contract making - a mental model. What this structure ensures is 'employ-ability' is never in doubt. What changes is the debits and credits. One employee may be hired at $100/hr (perhaps she holds a PhD) while another is hired at $6 an hour (a school drop out). Both gets hired and performs measurable tasks for the employer. This isn't a question of value-judging - it is about whether contract making is as flexible as possible that it allows a wide range of contracting possible.

Now, a complete third-party, the government, enters the fray. It begins to decide how inflexible the contract shall be henceforth. It says that no matter what the left side of the table is, the right side ought to contain the required $s. So, for instance a candidate has only a high school degree, no prior work experience, and has not-so-great track record, he shall be paid those $ values that is equally ascribed to someone else who is a graduate, has a few years of experience and has a clean track record in society.  This has several implications:

A lesser qualified candidate will find it harder to get a job

While he is willing to forgo $s for attributes he doesn't bring, the government doesn't allow him to take a lower wage. But the employer always has a choice whether to hire or not. The employer would vote with his vote by not hiring such a candidate.

Helps existing employees against those waiting to get hired

Minimum wage laws tend to build barriers to employment. The laws make the bargaining power of already employed stronger, while those who enter the industry would find it difficult to get a job. This is an unintended consequence of the law.

Unemployment increases

It is the experience of several countries that after introducing minimum wage laws, unemployment had soared. This is axiomatic as well. As price increases for a commodity, the demand for it reduces. Employers demand less labor as price is set higher. Despite the unpopularity from an economic standpoint, political reality is different. As a result, minimum wage law has found its way into several countries.

Minimum wage law does lesser damage when rates set are low

Many a times, minimum wage laws are not reset for inflation in regularity. In effect, these statutory wages are well below market-determined wages for long stretches of time. Thus it does much less harm. Yet, interns and temporary workers find it difficult to get jobs where wages are set from the perspective of full time employees.

Therefore, free markets perform a better job of matching candidates with appropriate wages. When governments meddle in the price forming process by arbitrarily declaring wages, without any sanctity to the terms of the contract, the contract making process is frustrated. Governments don't create jobs. It's the private sector that creates jobs. For that to happen seamlessly, an environment of encumbrance free contract making must be allowed to take place. Enforcing private contracts is the real job of any government. Not determining the debits and credits in a contract. Minimum wage laws alter contract terms to the detriment of both employers and employees who therefore desist from contracting. Unemployment increases and potential economic output remains unrealized.