Any type of cut or abrasion can get infected. You absolutely want to clean any wound thoroughly and keep an eye out for swelling and redness, which can both be signs of infection. The same is true for a wound that will not heal, that fills with pus or that seems tender and painful long after it should have healed.
That said, medical experts note that puncture wounds are more likely to get infected than common scrapes and bruises. There are a few reasons, the first of which is that it's very difficult to fully clean a puncture wound. While running it under soap and water may clean the surface, it may not do much for the deeper damage below the skin.
On top of that, the area inside the wound tends to be moist and warm. That is an ideal environment for bacteria. If you do not get it all the way cleaned out, you have simply given the remaining bacteria an optimal chance at survival.
Finally, when you're talking about animal bites like those you get from dogs and cats, you must remember that their mouth could be covered in bacteria and germs. This is not like a puncture wound from a new metal nail or a clean piece of glass. The odds of infection increase simply because it was an animal that injured you in the first place and their mouths carry bacteria.
If you do get bitten and it does get infected, it could lead to significant complications and the need for medical care. Make sure you are well aware of the rights you have to seek financial compensation.