Moral hazard refers to a situation where a person is more willing to take a risk if there is an assurance that the negative consequences will be taken care of by someone else. For example, a person with motor insurance is more likely to try to drive in a reckless manner; a business owner who has insurance to protect against any damage to machinery is less likely to take as much care to ensure it is not damaged than a person without insurance. If a government is willing to spend whatever is required to save banks from going bankrupt it makes the management of the banks take on larger risks like giving loans to people whose ability to repay the debt is not assured, not spending an extra amount to hedge their known risks, speculating in asset classes that could result in large losses, etc.
All good points. There was the element of theft as a moral hazard during the bank bailout. Banks, like businesses, must withstand the rigors of a Free Market. In doing so, they either survive and thrive, or die. Making foolish investments should have cost them; instead, the government picked up the tab.
If you don't like a particular bank, you can withdraw your money and go to another. In this case, the government took your money (through taxes) and without your consent, gave it to banks that it thought were worthy -- they effectively stole your money and gave it away to save those who caused the financial ruin.
One could argue that the more the government is involved in the economy, the greater of the risk of moral hazard. People might be less willing to make risky decisions if they were less confident that their mistakes would be "covered" by government bailouts. Some degree of government involvement in the economy is probably necessary and inevitable, but it is possible to argue that the trend has now gone too far -- at least if the American and European financial crises are any indication.
The whole concept of bailing out banks presents us with a real dilemma. How can there be any accountability for financial misdemeanours if those responsible for the financial crisis in which we find ourselves today are bailed out by government at the first sign of trouble in the offing? This does not promote responsible fiscal policies that will create economic wellbeing for all concerned. It rather encourages banks to take bigger and greater risks with the economy knowing that the taxpayer will help them out if they get it wrong. This is a massive moral hazard.
Moral hazard is when you know that it doesn't matter if you make mistakes. You know that someone will come and save you. So bailing out banks creates this. It gives the banks incentive to act recklessly and make dangerous loans because they banks can be sure that they will be bailed out with taxpayer money if their loans go bad.
A lemon market is when the seller know more about the product than the buyer. We can see this all the time in the markets. For example, if a company knows that it will have a bad few quarters, but they mislead investors by saying all is well, or when a firm cooks their books to make it seem the company is on the upswing when in fact it is on its way down.
In terms of your first question, many banks made risky moves knowing that there would be a bailout. And the fact that there was a bailout says that there will be others. To put it another way, if some banks are too big to fail, then they are even bigger now. The situation is ridiculous.