The main reason this is done is to save installation costs for the installer, along with saving the materials needed to pipe the intakes to the outside. All venting systems must be installed according to local gas codes and manufacturers installation instructions.
There is no real concerns with having the intake air being drawn from the inside of the structure.... in most cases. As long as your house does not severely go into negative pressure you will be fine. This will depend on how tightly your home is constructed. Most new homes do not come with the intake piped to the outside either. I have worked for many many large home builders, and when you are putting up 1000 homes, all they care about is saving the $100 dollars on each house.
The issues with having the intake air being taken from inside the envelope of the structure is that normally the intakes will suck up a lot of dust from the basement. Most people do not clean around the furnaces so that is usually the main cause, however if the area around the furnace, and the unit itself is cleaned regularly or yearly this will not really be an issue. The other issue with having this is when homeowners finish there basements. If a room is build around the furnace, you need to install 2 grills to supply fresh air to the room. In cases where this is not done, the furnace will starve for air and either shut down as a safety, or start running very inefficiently.
Those are the only real concerns with having the unit being piped inside of the house. I however still always recommend to have it done, and usually install it on every furnace installation i do, unless something is agreed upon with the homeowner. The main reason i do this is to not have to worry about homes going into negative pressure, and the fact that i can not control how people will be finishing there basements if they do in the future. Having the intake piped outside wont give you a noticeable increase in efficiency or energy savings by any means.
Now there are some minor draw backs with having the unit piped outside. When doing so you need to take extra time to make sure the intake is installed with proper clearances (whether it be to the outlet of the exhaust, or to the vent of the gas meter). The other thing you have to be aware of is that intake pipes, as well as exhaust pipes being blocked is a common thing. I have found literally everything imaginable inside of venting systems, and it is not a easy task to remove the blockage in most cases. Putting a piece 1/2" chicken wire will help to keep things from finding its way inside. Usually the cause is the homeowners children dropping rocks or balls into the vent. The other cause for a blocked vent may be animals, or an excessively high snow level. I do not recommend putting a tightly woven mesh, or any mesh that has holes less thats 3/8" in size. Doing so may cause a restriction in the intake pipe causing the furnace to shut down inadequate air supply. For the exhaust i would not use any mesh that had less that 1/2" holes. If a tightly woven mesh is used it will become saturated with water and then freeze when the furnace is on its off cycle. This would cause the furnace to shut down and lock out due to blockage in the venting.