I believe that the biggest pro about the Department of Homeland Security is safety and security. This department does much more than just keep us safe from things like terrorist threats though. It is really a very large department and consists of many different components including health affairs, nuclear detection, transportation security, customs and border protection, and immigration.
Really the only con I can see is that since there is a lot more security, for example at airports, it takes us longer to get through security lines. It also impedes on privacy. The way I see, it is worth it knowing that I am safer.
Below is the website for the Department of Homeland Security where you can find detailed information on everything that it does and is responsible for.
The first answer assumes that you are talking about the Department of Homeland Security as an organization. I assumed that you are talking about security in a generic sense and not about a particular bureaucratic organization.
If I am right, then the biggest pro would be security. It is, of course, a big pro to not have any successful terrorist attacks in our country.
A con that seems to go along with this security these days is increased inconvenience and intrusions on our privacy. This is most obvious in the elaborate procedures people have to to undergo when traveling by airplane.
Some of the pros are the potentials of the organization, the fact that they might be able to tie together the various intelligence agencies and increase communication between and among those groups leading to far more effective anti-terrorist work. This is something that the agencies are still struggling with and perhaps the dept. of homeland security will be able to fix it. They may also have helped with disaster readiness in many areas.
One of the major cons is the fact that much of its positive impact is still in the potential stage despite a huge influx of money and personnel. The agency has struggled to pull anything together, and has cost billions. It appears that it might be just one more bloated bureaucracy unless things change quickly.