Seafood is easy to determine: it must have both fins and scales. So whether "Oysters R In Season" or not, they are unfit for us to eat. Why? They're part of the ocean's sewage disposal system.
The use of parts of unclean animals in food preparation is also wrong. This eliminates the use of lard in cooking, or so-called clam juice in beverages. There is also an injunction against the ingestion of blood and fat of clean animals (Leviticus 3:11, 7:23-27). Therefore, even beef fat is to be avoided as a frying and cooking material.
A type of food not mentioned directly in the Bible are mushrooms. Recall God told Noah about the green herbs (Genesis 9:3). Mushrooms are fungus, not herbs, and neither are they green. According to "Dietary Carcinogens and Anticarcinogens" by Bruce Ames, mushrooms, even the supposedly edible kinds, contain cancer-causing agents.
You may wonder about scriptures which seem to say we can eat anything we want. This is not what the Bible says. Consider this: the Bible says when Christ returns, those who eat swine's flesh, and the abomination, and the mouse will be destroyed (Isaiah 66:15-17):
"For, behold, the LORD will come with fire, and with his chariots like a whirlwind, to render his anger with fury, and his rebuke with flames of fire. For by fire and by his sword will the LORD plead with all flesh: and the slain of the LORD shall be many. They that sanctify themselves, and purify themselves in the gardens behind one [tree] in the midst, eating swine's flesh, and the abomination, and the mouse, shall be consumed together, saith the LORD.
If all animals are now clean, this becomes an empty, meaningless threat.
We are to present our bodies as a living sacrifice (Romans 12:1-2), and should therefore keep them unpolluted. The body is the temple of the holy spirit, and God will destroy anyone who wilfully pollutes it (1Corinthians 3:16-17). The Christian's body, bought and paid for, is now the property of Jesus Christ, and is to be cared for as the owner directs (1Corinthians 6:19-20).