Is a corroded copper teapot safe?

It is currently a matter of opinion, not science, whether or not cooking hot foods in an unlined copper vessel leads to unheathy amounts of copper in the diet. Many health authorities caution against the use of pure copper even for cold drinks. However, it is demonstrably true that many, many people use pure copper vessels for cooking various foods and have done so for centuries, and Ayurvedic practitioners even consider water from copper pots to be healthier. And most of us have copper pipes, at least for hot water, and don't worry about it even though copper leaching from acidic water in pipes is a widespread health problem.

I was able to find lots of opinions on whether or not to use unlined copper vessels and kettles. This Fine Cooking article is typical of all of them. What a literature search does not turn up is any kind of actual science. National and regional health authorities seem to take it for granted that copper kettles leach toxic amounts of copper, and don't bother to test it, and everyone else seems to ignore them.

As such, as long as there's no history of Wilson's Disease in your family, I'd leave it up you. If you really like the kettle, use it. If you don't, then use something with no doubts attached -- and much easier to clean -- like stainless steel or ceramic.

Since this is a teapot and not a kettle (per comment), you do need to be careful of the acidity level of the teas you brew in it. Strongly acid teas will cause the kettle to corrode, and whether or not that results in unhealthy copper leaching (again, no science on this yet) it will discolor the pot and make it impossible to clean.

(And yes, copper is a nutrient in very small amounts. However, like many minerals, what's beneficial in tiny amounts is poisonous in larger ones. For example, as a ceramic artist I have to be careful with copper glazes in their raw form.)