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.