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Here is (conceivably incomplete) list of debugging and tracing output (but not 
error reporting) from C code.
Controlled output.
Import and shutdown details -- controlled by the -v flag.
Parser tracing -- controlled by the -d flag.
If Py_REF_DEBUG is defined -- controlled by the -X showrefcount flag.
If PYMALLOC_DEBUG is defined -- controlled by the PYTHONMALLOCSTATS environment 
variable.
If Py_TRACE_REFS is defined -- controlled by the PYTHONDUMPREFS environment 
variable.
Garbage collecting details -- controlled by gc.set_debug().
If LLTRACE is defined -- controlled by the __ltrace__ global variable.
Uncomtrolled output.
To stderr:
In PyType_ClearCache (Objects/typeobject.c) if MCACHE_STATS is defined.
Lists allocations if SHOW_ALLOC_COUNT is defined.
Tuples allocations if SHOW_TRACK_COUNT is defined.
Interned strings statistics if __INSURE__ is defined.
In Python/ceval.c if WITH_TSC is defined.
In _PyHash_Fini if Py_HASH_STATS is defined.
To stdout:
In Modules/_ctypes/malloc_closure.c if MALLOC_CLOSURE_DEBUG is defined.
Regex matching trace in Modules/_sre.c if VERBOSE is defined.
Statistics in Modules/hashtable.c if Py_DEBUG is defined.
Allocation counts if COUNT_ALLOCS is defined.
There is also dead code in Parser/parsetok.c, Parser/tokenizer.c, 
Python/pyarena.c, Python/compile.c, Python/formatter_unicode.c, 
Modules/_elementtree.c, Modules/_tkinter.c, Objects/unicodeobject.c.