Numbers with Rotational Symmetry
Python 2, 50 bytes

lambda n:`n`==`map('01xxxx9x86'.find,`n`)`[-2::-3]

The method '01xxxx9x86'.find takes a digit character to it's upside-down number, with any unflippable digit giving -1. This function is mapped to the reversed number string, producing a list of digits.
This is converted to a string with the [1::3] trick, except it's reversed instead by doing [-2::-3] (thanks to Dennis for this, saving 4 bytes),  and compared to the original number string. Any -1's from unflippable digits will misalign the conversion, making it fail.

56 bytes:
lambda n:`n`[::-1]==`n`.translate('01xxxx9x86______'*16)

Checks if the number string reversed is the same as it with the upside-down replacements. Digits that can't be flipped are replaced with 'x' to always give the wrong answer.
The replacement is done with translate on a string of 256 chars, replacing the corresponding ASCII values. Only the 10 values 48 to 57 matter, but I padded to length 16 to make the total length be 256. I wonder if there's a shorter way.
Some other approaches (lengths 59, 60, 60):
lambda n:set(zip(`n`,`n`[::-1]))&lt;=set(zip('01896','01869'))
r=lambda s:set(zip(s,s[::-1]));lambda n:r(`n`)&lt;=r('9018106')
lambda n:all(a+b in'001188969'for a,b in zip(`n`,`n`[::-1]))