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Bytes objects when indexed provide integers, but do not accept them to many functions, making them inconsistent with other sequences.
Basic example:
>>> test = b'012'
>>> n = test[1]
>>> n
49
>>> n in test
True
>>> test.index(n)
TypeError: expected an object with the buffer interface.
It is certainly unusual for n to be in the sequence, but not to be able to find it. I would expect the result to be 1. This set of commands with list, strings, tuples, but not bytes objects.
I suspect, from issue #10616, that all the following functions would be affected:
"bytes methods: partition, rpartition, find, index, rfind, rindex, count, translate, replace, startswith, endswith"
It would make more sense to me that instead of only supporting buffer interface objects, they also accept a single integer, and treat it as if it were provided a length-1 bytes object.
The use case I came across this problem was something like this:
Given seq1 and seq2, sequences of the same type:
[seq1.index(x) for x in seq2]
This works for strings, lists, tuples, but not bytes.

"This set of commands with list, strings, tuples, but not bytes objects."
should read
"This set of commands works with list, strings, tuples, but not bytes objects."

> It is certainly unusual for n to be in the sequence, but not to be able to find it.
Agreed. Doc Lib: 4.6. Sequence Types — str, bytes, bytearray, list, tuple, range says '''
s.index(i) index of the first occurence of i in s 
s.count(i) total number of occurences of i in s '''
so everything *in* a bytes should be valid for .index and .count.
>>> test = b'0120'
>>> z = b'0'
>>> zo = ord(z)
>>> z in test
True
>>> zo in test
True
>>> test.index(z)
0
>>> test.index(zo)
...
TypeError: expected an object with the buffer interface
>>> test.count(z)
2
>>> test.count(zo)
...
TypeError: expected an object with the buffer interface
# longer subsequences like b'01' also work
So I think the code for 3.2+ bytes.count() and bytes.index() should do the same branching as the code for bytes.__contains__.
The other functions you list, including .rindex are not general sequence functions but are string functions defined as taking subsequences as inputs. So they would never be used in generic code like .count and .index can be.

Fair enough.
I think it would make sense for the string methods to also accept single ints where possible as well:
For haystack and needles both strings:
[haystack.find(n) for n in needles]
For both bytes, it's a bit contortionist:
[haystack.find(needles[i:i+1]) for i in range(len(needles))]
One ends up doing a lot of the [i:i+1] bending when using bytes functions.

This affects bytearray as well as bytes.
What comes to supporting integer argument to str methods, I'm -1 on that. str's "contained items" are strings of length 1.

Attached a patch with the following changes:
Allow an integer argument in range(0, 256) for the following bytes and
bytearray methods: count, find, index, rfind, rindex. Initially, only
count and index were targeted, but as index is implemented in a helper
function that is also used to implement find, rfind and rindex, these
functions were affected too.
The bytes methods were changed to use the new buffer protocol instead
of the deprecated PyObject_AsCharBuffer, for consistency with the
bytearray code.
Tests for all the modified functions were expanded to cover the new
functionality. While at it, the tests for count, index and rindex were
also further expanded (to test for slices, for example), as they were
initially quite minimal.
A paragraph describing the additional semantics of the five methods
was added to the documentation.
The error messages of index and rindex were left untouched
("substring not found" and "subsection not found"). In a case where
the first argument is an integer, the error messages could talk about
a byte instead of substring/subsection. This would have been a bit
non-straightforward to implement, so I didn't.
The docstrings were also left unchanged, as I couldn't find a good
wording for them. The problem is not that the first argument may now
be an integer, but as it can now be more than a substring or
subsection, we might have to specify what a substring or subsection
really means. And that explanation would be lengthy (because of the buffer protocol, that's not a concept that a regular Python programmer is, or even needs to be, familiar with)...
And finally, there's one thing that I'm unsure of:
When an integer out of range(0, 256) is passed as the first argument,
should we raise a ValueError or a TypeError? Currently, a ValueError
is raised, but this may be bad for index and rindex, as they raise a
ValueError when the substring or byte is not found. I made the
decision to raise a ValueError decision because __contains__ of both
bytes and bytearray raise a ValueError when passed an integer not in
range(0, 256).

> When an integer out of range(0, 256) is passed as the first argument,
> should we raise a ValueError or a TypeError?
ValueError = Inappropriate argument value (of correct type).
TypeError = Inappropriate argument type.
> Currently, a ValueError raised, but this may be bad for index and 
> rindex, as they raise a ValueError when the substring or byte is not found.
Then the users should check if the value is in range(256) before passing it to (r)index.

Ok, so the current raising semantics should be good.

See also #12631 regarding the remove() method for bytearray.

> See also #12631 regarding the remove() method for bytearray.
AFAICS, it's about bytearray.remove() working but bytearray.index() not working as documented, and that's why I marked is as a duplicate of this issue.

> I made the
> decision to raise a ValueError decision because __contains__ of both
> bytes and bytearray raise a ValueError when passed an integer not in
> range(0, 256).
That sounds reasonable. OverflowError would have been another choice, but I agree that consistency with __contains__ is sensible.

Doc/library/stdtypes.rst needs a "versionadded" tag for the additional semantics.
Also, the patch doesn't compile fine on current default:
In file included from Objects/unicodeobject.c:487:0:
Objects/stringlib/find.h: In function ‘stringlib_parse_args_finds_byte’:
Objects/stringlib/find.h:158:5: attention : implicit declaration of function ‘stringlib_parse_args_finds’
In file included from Objects/unicodeobject.c:497:0:
Objects/stringlib/find.h: Hors de toute fonction :
Objects/stringlib/find.h:151:1: erreur: redefinition of ‘stringlib_parse_args_finds_byte’
Objects/stringlib/find.h:151:1: note: previous definition of ‘stringlib_parse_args_finds_byte’ was here
I'd say you need to either define your function as STRINGLIB(parse_args_finds_byte) (to avoid name collisions), or avoid defining it if STRINGLIB_IS_UNICODE.

Thanks for the review, Antoine. Attached an updated the patch:
- The function definition now uses STRINGLIB(...) and the function is only defined when !STRINGLIB_IS_UNICODE (so I took both approaches)
- Added a "versionadded:: 3.3" to the documentation.

Fixed a minor inconsistency.

New changeset c1effa2cdd20 by Antoine Pitrou in branch 'default':
Issue #12170: The count(), find(), rfind(), index() and rindex() methods
http://hg.python.org/cpython/rev/c1effa2cdd20 

Patch committed, thank you!

Just a thought: Would this change be worthy for the "What's new in 3.3" list?

> Just a thought: Would this change be worthy for the "What's new in 3.3" 
> list?
I think so.

New changeset 736b0aec412b by Petri Lehtinen in branch 'default':
Add a "What's New" entry for #12170
http://hg.python.org/cpython/rev/736b0aec412b 

New changeset 75648db1b3f3 by Victor Stinner in branch 'default':
Issue #13623: Fix a performance regression introduced by issue #12170 in
http://hg.python.org/cpython/rev/75648db1b3f3 

New changeset 75648db1b3f3 by Victor Stinner in branch 'default':
http://hg.python.org/cpython/rev/75648db1b3f3
Issue #13623: Fix a performance regression introduced by issue #12170 in bytes.find() and handle correctly OverflowError (raise the same ValueError than the error for -1).

New changeset 018fe1dee9b3 by Petri Lehtinen in branch 'default':
What's new: Add myself as the contributor of issue 12170
http://hg.python.org/cpython/rev/018fe1dee9b3