I get the following failures in a fresh checkout:

======================================================================
ERROR: test_explicit_relative_import (test.test_runpy.RunModuleTest)
----------------------------------------------------------------------

Traceback (most recent call last):
  File "/home/antoine/t/cpython/Lib/test/test_runpy.py", line 283, in test_explicit_relative_import
    self._check_relative_imports(depth)
  File "/home/antoine/t/cpython/Lib/test/test_runpy.py", line 257, in _check_relative_imports
    make_legacy_pyc(mod_fname)
  File "/home/antoine/t/cpython/Lib/test/support.py", line 217, in make_legacy_pyc
    os.rename(pyc_file, legacy_pyc)
OSError: [Errno 2] No such file or directory

======================================================================
ERROR: test_main_relative_import (test.test_runpy.RunModuleTest)
----------------------------------------------------------------------

Traceback (most recent call last):
  File "/home/antoine/t/cpython/Lib/test/test_runpy.py", line 288, in test_main_relative_import
    self._check_relative_imports(depth, "__main__")
  File "/home/antoine/t/cpython/Lib/test/test_runpy.py", line 257, in _check_relative_imports
    make_legacy_pyc(mod_fname)
  File "/home/antoine/t/cpython/Lib/test/support.py", line 217, in make_legacy_pyc
    os.rename(pyc_file, legacy_pyc)
OSError: [Errno 2] No such file or directory

======================================================================
ERROR: test_run_module (test.test_runpy.RunModuleTest)
----------------------------------------------------------------------

Traceback (most recent call last):
  File "/home/antoine/t/cpython/Lib/test/test_runpy.py", line 273, in test_run_module
    self._check_module(depth)
  File "/home/antoine/t/cpython/Lib/test/test_runpy.py", line 177, in _check_module
    make_legacy_pyc(mod_fname)
  File "/home/antoine/t/cpython/Lib/test/support.py", line 217, in make_legacy_pyc
    os.rename(pyc_file, legacy_pyc)
OSError: [Errno 2] No such file or directory

======================================================================
ERROR: test_run_package (test.test_runpy.RunModuleTest)
----------------------------------------------------------------------

Traceback (most recent call last):
  File "/home/antoine/t/cpython/Lib/test/test_runpy.py", line 278, in test_run_package
    self._check_package(depth)
  File "/home/antoine/t/cpython/Lib/test/test_runpy.py", line 201, in _check_package
    make_legacy_pyc(mod_fname)
  File "/home/antoine/t/cpython/Lib/test/support.py", line 217, in make_legacy_pyc
    os.rename(pyc_file, legacy_pyc)
OSError: [Errno 2] No such file or directory

Here is the test output:

test_run_code (test.test_runpy.RunModuleCodeTest) ... ok
test_run_module_code (test.test_runpy.RunModuleCodeTest) ... ok
test_explicit_relative_import (test.test_runpy.RunModuleTest) ... Testing relative imports at depth: 2
Package tree in: /tmp/tmpmruwyg
Updated sys.path: /tmp/tmpmruwyg
Next level in: /tmp/tmpmruwyg/runpy_pkg
Created: /tmp/tmpmruwyg/runpy_pkg/init.py
Next level in: /tmp/tmpmruwyg/runpy_pkg/runpy_pkg
Created: /tmp/tmpmruwyg/runpy_pkg/runpy_pkg/init.py
Created: /tmp/tmpmruwyg/runpy_pkg/runpy_pkg/runpy_test.py
Added sibling module: /tmp/tmpmruwyg/runpy_pkg/runpy_pkg/sibling.py
Added uncle package: /tmp/tmpmruwyg/runpy_pkg/uncle
Added cousin package: /tmp/tmpmruwyg/runpy_pkg/uncle/cousin
Added nephew module: /tmp/tmpmruwyg/runpy_pkg/uncle/cousin/nephew.py
Running from source: __runpy_pkg__.__runpy_pkg__.runpy_test
Removed sys.modules entries
Removed sys.path entry
Removed package tree
ERROR
test_invalid_names (test.test_runpy.RunModuleTest) ... ok
test_library_module (test.test_runpy.RunModuleTest) ... ok
test_main_relative_import (test.test_runpy.RunModuleTest) ... Testing main relative imports at depth: 2
Package tree in: /tmp/tmp39sx5n
Updated sys.path: /tmp/tmp39sx5n
Next level in: /tmp/tmp39sx5n/runpy_pkg
Created: /tmp/tmp39sx5n/runpy_pkg/init.py
Next level in: /tmp/tmp39sx5n/runpy_pkg/runpy_pkg
Created: /tmp/tmp39sx5n/runpy_pkg/runpy_pkg/init.py
Created: /tmp/tmp39sx5n/runpy_pkg/runpy_pkg/runpy_test.py
Added sibling module: /tmp/tmp39sx5n/runpy_pkg/runpy_pkg/sibling.py
Added uncle package: /tmp/tmp39sx5n/runpy_pkg/uncle
Added cousin package: /tmp/tmp39sx5n/runpy_pkg/uncle/cousin
Added nephew module: /tmp/tmp39sx5n/runpy_pkg/uncle/cousin/nephew.py
Running from source: __runpy_pkg__.__runpy_pkg__.runpy_test
Removed sys.modules entries
Removed sys.path entry
Removed package tree
ERROR
test_run_module (test.test_runpy.RunModuleTest) ... Testing package depth: 0
Package tree in: /tmp/tmpy4y7in
Updated sys.path: /tmp/tmpy4y7in
Created: /tmp/tmpy4y7in/runpy_test.py
Running from source: runpy_test
Removed sys.modules entries
Removed sys.path entry
Removed package tree
ERROR
test_run_package (test.test_runpy.RunModuleTest) ... Testing package depth: 1
Package tree in: /tmp/tmp_7dx_4
Updated sys.path: /tmp/tmp_7dx_4
Next level in: /tmp/tmp_7dx_4/runpy_pkg
Created: /tmp/tmp_7dx_4/runpy_pkg/init.py
Created: /tmp/tmp_7dx_4/runpy_pkg/main.py
Running from source: __runpy_pkg__
Removed sys.modules entries
Removed sys.path entry
Removed package tree
ERROR
test_basic_script (test.test_runpy.RunPathTest) ... ok
test_directory (test.test_runpy.RunPathTest) ... ok
test_directory_compiled (test.test_runpy.RunPathTest) ... ok
test_directory_error (test.test_runpy.RunPathTest) ... ok
test_main_recursion_error (test.test_runpy.RunPathTest) ... ok
test_script_compiled (test.test_runpy.RunPathTest) ... ok
test_zipfile (test.test_runpy.RunPathTest) ... ok
test_zipfile_compiled (test.test_runpy.RunPathTest) ... ok
test_zipfile_error (test.test_runpy.RunPathTest) ... ok

It still works fine for me (as do test_imp, test_import and test_importlib).

Did you provide any arguments to ./configure, or provide any interesting options to regrtest to get it to fail?

Oh, that's the other question - is there any chance you are passing -B or have PYTHONDONTWRITEBYTECODE set? (I'm not sure that would affect make_legacy_pyc, but all the errors you posted relate to unexpectedly absent pyc files and directories)

Indeed, PYTHONDONTWRITEBYTECODE seems set by default on this Linux install... Ouch.

Duplicate of bpo-12117.