Humans get sick on such a regular basis and animals will hardly ever get sick. Animals are typically exposed to the same pathogens as humans, yet a dog won't have a cold or the flu twice a year, with other miner health issues occurring regularly in between. I understand that humans are very structurally flawed due to some evolutionary processes, and I'm just wondering why our immune systems seemed to have taken a pretty big hit as well.
The question probably has a mistaken premise. Human immune systems are pretty similar to other species, at least in major structural elements. Our differences in adaptive niche have led to differences in some aspects; humans don't fare well with rotting meat, for example, while a scavenger can eat it without a problem. Many scavengers have unique adaptations for dealing with this. Dogs do not, however. Humans too have a unique niche, which is highly social, and thus have a well-developed social immunity (sometimes called a behavioral immune system).
Many animal populations have endemic diseases at fairly high levels. Koalas, for example, famously have a very high level of chlamydia. Sea lions rookeries often have infections, bats can have high levels of rabies, and so forth. Lots of animals do get lots of infections.
However your question specifically on dogs is interesting, and probably gets to a risk factor which is very human. Humans come into contact with far more other humans (and thus, likely more infected humans) than dogs encounter other dogs. Diseases which spread through close proximity, such as airborn upper respiratory viruses, spread more readily in humans than these relatively isolated animal populations. Combine that with a concerted effort to wipe out in animals any diseases which can transmit to humans, and pet infections are indeed relatively rare. This is not due to the immune system per se, but the social factors associated with each organisms' niche.