I don't know any tool that can do what you want. You can write your function as fault tolerant - you can trap errors, and you can print a some messages.
I am aware of the edb-debugger that one can use with pgadmin for debugging functions. However, I am looking for a solution that doesn't involve such additions to the server. I'm using a function in a SELECT query, but it's failing for some rows in a very large table. By using LIMIT and OFFSET I see that it runs fine for some parts of the table. Is there some way to print the rows where it fails? For now, I've simply modified the function to return a value that I can use in the SELECT query to filtering, but I'm wondering whether there's a parameter or setting that would accomplish the same thing without modifying the function.
