This is a complicated question, as it deals with both chemical and microbial contaminants.

Chemical contaminants can indeed be present in milk and dairy products, just as in any other natural product. In the case of milk, these contaminants are transported through the cow, which ingests contaminants from the environment through the grass. The contaminants are largely excreted through the urine and faeces, partly inactivated and destroyed in the liver, and a part may be excreted through the milk.
It is impossible to list these contaminants, as there are so many factors and compounds involved. Also, many of these compounds will be in the lipid fraction of the milk, hence the fat percentage of the milk plays an important role. Contamination of milk and the diversity of the possible contaminants are, of course, not restricted to cow's milk, but can be found in all mammalian milk, including human and goat's milk. Seal milk, for example, contains a lot of PCB's that accumulate in the fat fraction of the milk; as seal milk contains a lot of fat, there is a high level of PCB's and similar contaminants in it .
Human milk often contains residues of medicines taken by the mother during or after pregnancy. Veterinary medicines thus are one of the many groups of chemical contaminants that may be present in milk. Chemical contaminants are not only of human origin, but natural toxins (from plants or fungi) may also be present in milk.

The other group of possible contaminants in foods, including milk, consists of substances of microbial origin . Milk is sterile as long as it is in the body. It will immediately be contaminated by bacteria from the skin and the environment (babies acquire their intestinal flora also through contamination in the birth channel and mother's skin). Which micro organisms may be present thus depends on the environment.
As micro organisms grow faster at high temperatures, milk is kept as much as possible at refrigeration temperatures. In the dairy industry milk will normally be pasteurised. This process involves heating at 80 degrees Celsius for a limited time. Practically all vegetative cells will be killed, with the exception of spores. As the milk is not completely sterile, the residual bacterial spores may start to germinate and multiply again. Hence the milk should be kept refrigerated at all times, until it is on the consumer's table.
Part of the milk will also be sterilised, that is, heated at temperatures above 100 degrees Celsius. During this treatment all living bacteria and spores are killed. Sterilised milk thus has a very long shelf life and does not require refrigeration until opened. After opening the package it will be re-contaminated by micro organisms from the environment and thus has to be kept refrigerated.
All fresh milk in the EU is either pasteurised or sterilised and thus consumers are not at risk of becoming ill due to Salmonella or Listeria . As nearly all dairy products are made from pasteurised milk, there is no risk either. Only raw milk and some cheeses made from raw milk can be considered a risk for these bacteria.