Inconsistent and Hard-to-reproduce Issues with Null Index Values
### Code Sample, a copy-pastable example if possible

```python
# Note:  This is not real Python code.  I can't reproduce these problems with toy data, but they
# show up consistently with certain sets of real data.

from pandas import Series
vocabulary = Series(data = <a few thousand integers>, index = <a few thousand words/tokens, including u"null">)
new_vocab = Series(data = <a smaller list of integers>, index = <a smaller list of words, mostly overlapping with the first one, also including u"null">)
new_words = new_vocab.index.difference(vocabulary.index)

print u"null" is in vocabulary.index
print u"null" is in new_vocab.index
print u"null" is in new_words

> True
> True
> True


from pandas import DataFrame
matrix1 = DataFrame(data = <a bunch of numbers>, index = <list of topic names>, columns <list of words/tokens, _not_ including NaN or u"nan">)
matrix2 = DataFrame(data = <a bunch of numbers>, index = <list of topic names>, columns <list of words/tokens, _not_ including NaN or u"nan">)
matrix3 = matrix1.multiply(matrix2)

from numpy import NaN
print NaN in matrix1.columns
print u"nan" in matrix1.columns
print NaN in matrix2.columns
print u"nan" in matrix2.columns
print NaN in matrix3.columns
print u"nan" in matrix3.columns

> False
> False
> False
> False
> True
> True
```
#### Problem description

This may be related to #18988.

I feel bad about reporting these bugs, because I can't duplicate them outside actual scripts with actual (rather voluminous) data.  The first common denominator to all the issues is that when I perform operations involving two objects, I end up with extra columns (in DataFrames) or elements (in Series or Indexes):  sometimes duplicates of existing columns (but the second, duplicate column will contain all null values), sometimes entirely new columns/elements.

The second common denominator is that every case seems to involve "null-like" index values:  NaN, u"nan", u"null", u"n/a", and u"null.1.1" are the ones I've actually observed.  In one case, u"null" creates a problem; in another u"null" works just fine, while u"n/a" and u"null.1.1" create problems (but u"null.1" doesn't).  In a third case, the null-like values don't exist in the original objects, but show up after an operation, as new columns (interestingly, in this case, under pandas 20.3 I got two columns, NaN, and u"nan", while in pandas 22.0, I get those two plus u"n/a"--or actually, the "len" function is telling me there are four extra columns, but I using a "difference" method only gives me a list of three)--and they show up with some sets of data but not others.

In each case where errors have shown up, I've added code to check for them and remove the spurious columns/elements, but it's been very frustrating to run down different problem that can occur.
#### Output of ``pd.show_versions()``

<details>

[paste the output of ``pd.show_versions()`` here below this line]
INSTALLED VERSIONS
------------------
commit: None
python: 2.7.14.final.0
python-bits: 64
OS: Windows
OS-release: 10
machine: AMD64
processor: Intel64 Family 6 Model 94 Stepping 3, GenuineIntel
byteorder: little
LC_ALL: None
LANG: en
LOCALE: None.None

pandas: 0.20.3
pytest: 3.2.1
pip: 9.0.1
setuptools: 38.4.0
Cython: 0.26.1
numpy: 1.13.3
scipy: 1.0.0
xarray: None
IPython: 5.4.1
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: 2.6.4
feather: None
matplotlib: 2.1.0
openpyxl: 2.4.8
xlrd: 1.1.0
xlwt: 1.3.0
xlsxwriter: 1.0.2
lxml: 4.1.0
bs4: 4.6.0
html5lib: 1.0.1
sqlalchemy: 1.1.13
pymysql: None
psycopg2: None
jinja2: 2.9.6
s3fs: None
pandas_gbq: None
pandas_datareader: None
</details>
