If a cow is fed animal by products, including pig parts, could its meat still be made kosher?
Yes, cows are not required to keep kosher.
Similarly, a kosher fish that has been caught in the ocean may be eaten, even though it may have eaten a non-kosher fish. Once something is consumed, it is usually considered a bona-fide part of the animal and may be eaten.
(That said, there are some authorities who rule that if a whole non-kosher fish is found inside a kosher fish (i.e. it was just eaten right before it was caught) it (the non-kosher fish) should be discarded.)
Zev Steinhardt
Fogive me if I’m picking nits, but is there such a thing as a non-kosher fish? I thought that anything that lived in the water and had fins and scales (pretty good description of a fish there) was OK. Do you mean non-kosher (non-fish) sea life, like crustaceans and mollusks?
I believe that bottom-feeders and fish that look more like skin than scales are non-kosher. This is just a vague memory from high school history class.
Not all fish have scales, and not all scales are indicative of kosher fish. The most famous example of a non-kosher fish that I can currently think of is a shark.
Only fish with cycloid or ctenoid scales are kosher.
Zev Steinhardt
…and, of course, a lobster who eats only kosher food all his poor little life, will never himself be kosher… regardless of his diet.
Even if the fish he eats is a gefilte? 
Zev Steinhardt
I wouldn’t exactly call the lobster “poor”, though… After all, if he’s not kosher, there’s that many less people trying to eat him, which is probably not a bad thing, from the lobster’s point of view.
I have a new theory. You know why people keep asking these kosher questions? Because there are always answers to them. Some rabbi, some time, some where, sat down and figured out the rules for every possible gray area. Probably to keep the annoying kids in Hebrew school quiet with the questions all the time.
This is why we like these questions, because the answers are so ingenious!
Here’s another question waiting for an ingenious answer:
The other day someone was talking about the no meat at the same time as cheese rule, and explained it as “You don’t boil the baby in mother’s milk”. Now this conversation wasn’t in a serious context, and I know NOTHING about the rules about kosher stuff, but at the time, the question had to be asked:
What if it’s beef and goat cheese. Not the same animal, what do you say to that?
The guy just rolled his eyes and didn’t answer.
So what does the rabbi-who-made-the-rules have to say to that? LOL
mnemosyne:
Actually, I think that from strictly Biblical law (correct me if I’m wrong, Zev, Izzy, CK - ), milk and meat of different species are permitted, but that the Rabbis forbade that mixture because it’s too easy to forget and end up eating the actual prohibited same-species mixture.
The prohibition has a much broader context than simply a “kid in it’s mother’s milk.” All milk-meat mixtures are forbidden.
Zev Steinhardt
Can’t resist this one . . .
“A Dialogue While Moses Is At The Top Of Mt. Sinai…”
G-d: And remember Moses, in the laws of keeping
Kosher, never cook a calf in its mother’s milk. It is
cruel.
Moses: Ohhhhh! So you are saying we should
never eat milk and meat together.
G-d: No, what I’m saying is, never cook a calf in
its mother’s milk.
Moses: Oh, Lord forgive my ignorance! What you
are really saying is we should wait six hours after
eating meat to eat milk so the two are not in our
stomachs.
G-d: No, Moses, listen to me. I am saying, don’t
cook a calf in its mother’s milk!!!
Moses: Oh, Lord! Please don’t strike me down
for my stupidity! What you mean is we should
have a separate set of dishes for milk and a
separate set for meat and if we make a mistake
we have to bury that dish outside…
G-d: Moses, do whatever you want…
Just to clarify the background of a law that might sound unbased:
Jewish ritual law contains two parts, both of which were transmitted to Moses at Sinai: The written Law (i.e., the Five Books of Moses), and the Oral Law (which some 1700 years ago was partially codified into works such as the Talmud and Midrash). The Oral Law, which was originally passed down orally (hence the name), serves as an explanation, clarification, and expansion of the laws introduced in the Written law. The Written Law simply says “Thou shalt not seethe a kid in its mother’s milk”, in three different places (I believe once in Exodus, once in Leviticus, and once in Deuteronomy). The Oral tradition explains that this repetition is a reference to three different prohibitions involving mixtures of meat and milk, one of which is ingestion.