The Critic

This person likes to put down anything and anybody. They will criticize minor mistakes and pick apart your food,
your staff, etc.

How can you deal with them?

Carrie Mason-Draffen, author of 151 Quick Ideas to Deal With Difficult People, writes that this type of person grew up around negativity.
They were probably criticized by their parents or others, and developed a negative attitude by replicating what they heard.

These people will wear you down if you keep listening to their continuous complaints about everything - from the way your napkins are folded to the temperature of the food to a two-minute delay in the delivery of their appetizers.

You must remember that these complaints may be directed at your place or your staff, but the root of the dissatisfaction is not in your restaurant.
These people are just venting their unhappiness and negativity at your establishment. 

Ask your waiters to try to diffuse the negativity by responding with understanding and saying something positive. For instance, if your Critic claims that the food is cold then your staff can respond by saying, "I'm sorry about that. I will bring it back to the kitchen, warm it up and get it right back to you."

Remind your staff to always be positive in their attitude, and not to take the criticism personally. Critics thrive in conflict and they look for it. You owe it to your other customers to keep a nice, relaxed ambience. If they see that, despite these complaints, your staff is trying to correct the situation and keeping a positive attitude, they will value your place even more.

Please notice that I am talking here about a person with a pattern of negativity, not an angry customer that may be reasonably upset because of
a specific dining issue.

"One of the best ways to deal with an angry person is to actively listen to what they are saying," says Elizabeth Stanczak, executive director of UTSA's health and counseling services. "Often the angry person is frustrated because they don't believe they are being heard and think no one wants to help them."

Always try to listen first to your customers if they are angry. They may have a reason that can be easily solved. Listen to what they have to tell you,
and try to come up with a satisfactory solution. This often diffuses their anger and leaves everybody happy. However, if you see that these people are purposely disruptive, politely ask them to leave your place and suggest they come back when they feel less upset. Tell them something like:

"I'm sorry you are not enjoying yourself. Perhaps you should leave tonight and we can start over another time. Since you haven't enjoyed your time here, your meal is on the house."

Although you may feel tempted to get your money from these ungrateful people, don't charge them for the meal. This will likely start a big argument
or allow them to make another negative comment.

These people are looking for an excuse to validate their negativity, and asking them to pay while inviting them to leave will provoke their fury.
They will make a scene, and will make the dining experience very unpleasant for the rest of your clients. You can't win this battle.

However, if you ask them to leave with no charges you lose the cost of the food and drinks, but you save the reputation of your restaurant and you ensure that other diners will recognize your willingness to accommodate your disruptive Critic.

Source : http://www.ezinearticles.com/?How-to-Deal-With-Difficult-Restaurant-Customers&id=2049544