It's pretty common to find coins with problems. Whether these fit your collecting needs or not depends on a variety of factors.

What is the problem, how bad is it? Where is the problem and will it affect your ability to enjoy the coin? Has the price been adjusted to reflect the problem?

Here are some common problems you're likely to encounter:

MARKS, CUTS AND SCRATCHES.
These are man-made flaws, not created by circulation or handling at the mint. Often these imperfections are the result of mishandling a coin.

Marks, cuts and scratches which are large and/or in the focal area of the coin are significant problems. The experienced collector expects to see more marks on the average silver dollar than on a smaller coin such as a Mercury Dime. In other words, allowance is generally made for some minor marks, cuts and scratches on the larger coins; these are calculated into the grade. A large staple scratch across a coin is always a deduct.

RIM NICKS AND BUMPS.
Such imperfections are often acquired through circulation, occasionally from mishandling.

Rim imperfections should be assessed in proportion to the size of the coin. A small coin, like an Indian Cent, may have a small nick which will be extremely visible since the coin is relatively small. Conversely, on a Morgan Dollar a similar rim nick may be barely noticeable due to the relatively large size of the coin.

CLEANED COINS.
Many coins have been cleaned at some time in their existence. Coins which have been cleaned gently and appropriately are encountered every day -- so are coins which have been cleaned harshly and inappropriately. How do you know when cleaning is a problem?

Cleaning is a problem when it significantly reduces the eye appeal of the coin. For instance, if a Morgan Dollar has been cleaned with an abrasive substance like baking soda, many hairline scratches result. Perhaps the dollar was cleaned with a substance that damaged the surface, leaving a gray, dead look where one might expect to see lustre (on a higher grade coin, for instance).

On copper coins, harsh cleaning often results in an unnatural, bright red color.

POROSITY OR CORROSION.
Porosity or corrosion are created by a variety of situations: a coin was buried in the ground; it was contaminated by water or foreign substances (such as acid, lye or paint).

Porosity or corrosion describe surface damage which may range from light to heavy. The problem is usually permanent. Sometimes porosity or corrosion greatly affect eye appeal, sometimes hardly at all.

These are problems inherent to copper coins with their soft surfaces. Half Cents and Large Cents are especially prone to porosity and corrosion. While still a deduction in grade and price, the market is very active in nice coins with these problems.

PRICING OF PROBLEM COINS.
A big scratch, initials, large or numerous rim nicks, or harsh cleaning will always reduce the price by half or more. On the other hand, a small scratch, minor rim nick or very light cleaning may result in no more than a 20% price reduction.

Porosity or corrosion is always a price reduction -- exactly how much depends on severity of the condition and overall eye appeal of the coin.