Issue 1:
Code Sample, a copy-pastable example if possible

In [97]: s1 = pd.Series([1,2,3], index=[4,5,6])

In [98]: s2 = pd.Series([1,3,2], index=s1)

In [99]: s2
Out[101]:
1 1
2 3
3 2
dtype: int64

so far so good, now lets try a boolean series

In [101]: s3 = pd.Series([1,3,2], index=(s1==2))

In [102]: s3
...
...
~/anaconda3/lib/python3.5/site-packages/pandas/core/indexes/base.py in _format_with_header(self, header, na_rep, **kwargs)
1905 values = np.array(values)
1906 elif is_object_dtype(values.dtype):
-> 1907 values = lib.maybe_convert_objects(values, safe=1)
1908
1909 if is_object_dtype(values.dtype):

TypeError: Argument 'objects' has incorrect type (expected numpy.ndarray, got Series)

In [103]: s3.index
...
...
~/anaconda3/lib/python3.5/site-packages/pandas/core/indexes/base.py in inferred_type(self)
1567 def inferred_type(self):
1568 """ return a string of the type inferred from the values """
-> 1569 return lib.infer_dtype(self)
1570
1571 def _is_memory_usage_qualified(self):

pandas/_libs/src/inference.pyx in pandas._libs.lib.infer_dtype (pandas/_libs/lib.c:47002)()

ValueError: cannot infer type for <class 'NoneType'>

now a dataframe

In [178]: df = pd.DataFrame([[1,2],[3,4],[5,6]], index=[3,6,9])

In [180]: s4 = pd.Series([1,3,2], index=df)

In [181]: s4
...
...
~/anaconda3/lib/python3.5/site-packages/pandas/io/formats/format.py in <lambda>(x)
1967
1968 def _format_strings(self):
-> 1969 formatter = self.formatter or (lambda x: '% d' % x)
1970 fmt_values = [formatter(x) for x in self.values]
1971 return fmt_values

TypeError: %d format: a number is required, not numpy.ndarray

In [182]: s4.index
Out[182]: Int64Index([[1, 2], [3, 4], [5, 6]], dtype='int64')

Problem description

I would expect passing a boolean Series as the index= parameter to either act as Series.index (as in the example where the integer Series s1 is used as an index) or Series.values (as the docs seem imply http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.html "index : array-like or Index (1d)")

For the DataFrame case, it could either use df.index, or fail early with a ValueError

[this should explain why the current behaviour is a problem and why the expected output is a better solution.]

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Expected Output

either

In [101]: s3 = pd.Series([1,3,2], index=(s1==2))
In [102]: s3
Out[119]:
4 1
5 3
6 2
dtype: int64

In [103]: s4 = pd.Series([1,2,3], index=df)
In [104]: s4
Out[104]:
4 1
5 2
6 3
dtype: int64

OR

In [121]: s3
Out[121]:
False 1
True 3
False 2
dtype: int64

s4 = pd.Series([1,3,2], index=df)
ValueError

Output of pd.show_versions()

[paste the output of pd.show_versions() here below this line]

INSTALLED VERSIONS

commit: None

python: 3.5.4.final.0

python-bits: 64

OS: Darwin

OS-release: 17.2.0

machine: x86_64

processor: i386

byteorder: little

LC_ALL: None

LANG: en_GB.UTF-8

LOCALE: en_GB.UTF-8

pandas: 0.20.3

pytest: 3.2.1

pip: 9.0.1

setuptools: 36.4.0

Cython: 0.26

numpy: 1.12.1

scipy: 0.19.1

xarray: None

IPython: 6.1.0

sphinx: 1.6.3

patsy: 0.4.1

dateutil: 2.6.1

pytz: 2017.2

blosc: None

bottleneck: 1.2.1

tables: 3.4.2

numexpr: 2.6.2

feather: None

matplotlib: 2.0.2

openpyxl: 2.4.8

xlrd: 1.1.0

xlwt: 1.3.0

xlsxwriter: 0.9.8

lxml: 3.8.0

bs4: 4.6.0

html5lib: 0.9999999

sqlalchemy: 1.1.13

pymysql: None

psycopg2: None

jinja2: 2.9.6

s3fs: None

pandas_gbq: None

pandas_datareader: None

Issue 2:
>>> d = pandas.Series({('1ab','2'): 3, ('1ab',3):4}, )
>>> d = pandas.concat([d,d])
>>> d = pandas.concat([d,d], axis=1)
>>> pickle.loads(pickle.dumps(d))
0 1
1ab 3 4 4
2 3 3
3 4 4
2 3 3
>>> pickle.loads(pickle.dumps(d.T))
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/usr/lib64/python2.7/pickle.py", line 1382, in loads
return Unpickler(file).load()
File "/usr/lib64/python2.7/pickle.py", line 858, in load
dispatch[key](self)
File "/usr/lib64/python2.7/pickle.py", line 1217, in load_build
setstate(state)
File "venv/lib/python2.7/site-packages/pandas/core/internals.py", line 2063, in __setstate__
placement=self.axes[0].get_indexer(items))
File "venv/lib/python2.7/site-packages/pandas/core/index.py", line 3200, in get_indexer
raise Exception('Reindexing only valid with uniquely valued Index '
Exception: Reindexing only valid with uniquely valued Index objects