Food hierarchy and food web
Ecological trophic interactions are better represented by food webs rather than simple hierarchical relationships. As a consequence, the concepts of primary/secondary/tertiary/... consumers sometimes poorly apply to reality.
Obligate and Optional
Many species are able to feed on a various source of nutrients. As a consequence, a species can be a primary consumer under one environmental condition and be a secondary consumer under another. Such species might eventually almost never be both a primary and a secondary consumer at the same time and it renders the classification of species into one or another category a little more arbitrary.
How much does one need to eat to belong to a given category?
Note also that species like the cat, for example, are generally considered as being just carnivorous while in reality they often eat a very small amount of plant material. They also indirectly consume plant materials that are present within the gut of their preys. Such cases make the categorization more arbitrary again
Primary, secondary and tertiary consumer
This one is pretty easy. Humans, pigs, bears, corvids and catfish are all examples of species that are primary, secondary and tertiary consumer all in the same time. In other words, humans are omnivorous.
I am currently preparing a stew for tonight $\ddot \smile$. There are a number of vegetables and a little bit of pork (which itself is omnivorous). Tomorrow, I'll make some salmon (which is a secondary consumer as it mainly feeds on zooplankton).
Producer and secondary consumer
Carnivorous plants are able to photosynthesize and to capture animals. Most animals they capture are often best described as a primary consumer but some carnivorous plants small fish that feed on phytoplankton or even mice and frogs according to this video.
Producer and primary consumer
Parasitic plants (such as the common holly) are able to both photosynthesize and parasitize other primary consumers (it therefore also is a primary consumer if we equate parasitism to consumerism).
The eastern emerald elysia (a sea slug) feed on algae and is able to photosynthesize (using the chloroplasts of its preys).
Producer, primary consumer and secondary consumer
I cannot think of any examples right now but I would bet that it exists (eventually in a chemoautotroph species and eventually in a species that has a various life cycle).