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Hello,
The bug occurs when writing an XML file using the UTF-16 encoding.
The problem is that the etree encodes every string to utf-16 by itself - meaning, inserting the 0xfffe BOM before every string (tag, text, attribute name, etc.), causing a badly formed utf=16 strings.
A possible solution, which was offered by a co-worker of mine, was to use a utf-16 writer (from codecs.getwriter('utf-16') to write the file.
Best,
BugoK.

Fredrik, could you take a look at this?

ET's standard serializer currently only supports ASCII-compatible encodings. See e.g.
 http://effbot.python-hosting.com/ticket/47
The best workaround for ET 1.2 (Python 2.5) is probably to serialize as "utf-8" and transcode:
 out = unicode(ET.tostring(elem), "utf-8").encode(...)

This is a bug in two halves.
1. Not all characters in the file are UTF-16. The initial xml header
isn't, and the individual < > etc characters are not. This is just a
matter of extending the methodology to encode all characters and not
just the textual bits. There is no work-around except a five-minute hack
of the ElementTree.write() method.
2. Every write has a BOM, so corrupting the file in a manner analogous
to bug 555360. This is a result of using string.encode() and is a
well-known feature. It can be worked around by using UTF-16LE or
UTF-16BE which do not prepend a BOM, but then the file doesn't have any
BOM. A complete solution would be to rewrite ElementTree.write() to use
a different encoding methodology such as StreamWriter.
I have made the above hack and work-around for my own use, and I can
report that it produces perfect UTF-16.

Would you provide a patch?

Here is a patch of my quick hack, more for interest than any suggestion
it gets used. Although it does produce good output so long as you avoid
the BOM.
The full solution is beyond my (very weak) Python skills. The character
encoding is tied in with XML character substitution (& etc. and
hexadecimal representation of multibyte characters). I could disentangle
it, but I probably wouldn't produce optimal Python, or indeed anything
that wouldn't inspire mirth and/or incredulity.
NB. The workaround suggested by Fredrik Lundh doesn't solve our
particular problems, since the downsize to UTF-8 causes the multi-byte
characters to be represented in hex. Our software doesn't read those. (I
know that's our problem.)

Could you provide a test case, so we can check if the upgrade proposed on #6472 solves this issue?

@Richard: Could you provide a test case for this, or do you consider it beyond your Python capabilities allowing for your comments on msg75875?

I can't produce an automated test, for want of time, but here is a demonstrator.
Grab the example XHTML from http://docs.python.org/library/xml.etree.elementtree.html#elementtree-objects or use some tiny ASCII-encoded xml file. Save it as "file.xml" in the same folder as bug-test.py attached here.
Execute bug-test.xml
file.xml is read and then written in UTF-16. The output file is then read and dumped to stdout as a byte-stream.
1. To be correct UTF-16, the output should start with 255 254, which should never occur in the rest of the file.
2. The rest of the output (including the first line) should alternate zeros with ASCII character codes.
3. The file output.xml should be loadable in a UTF16-capable text editor (eg jEdit), be recognised as UTF-16 and be identical in terms of content to file.xml

> Execute bug-test.xml
I meant bug-test.py, of course

@Florent: is this something you could pick up, I think it's out of my league.

As an example, here is the first two lines of output when I use Python 2.6.3:
60 63 120 109 108 32 118 101 114 115 105 111 110 61 39 49 46 48 39 32 101 110 99 111 100 105 110 103 61 39 85 84 70 45 49 54 39 63 62 10
60 255 254 104 0 116 0 109 0 108 0 62 255 254 10
Note:
No 255 254 at the start of the file, but several within it.
No zeros interspersing the first line and the odd one missing thereafter.

Python 3.1 improves the situation, the file looks more like utf-16, except that the BOM ("\xff\xfe") is repeated all the time, probably on every internal call to file.write().
Here is a test script that should work on both 2.7 and 3.1.
from io import BytesIO
from xml.etree.ElementTree import ElementTree
content = "<?xml version='1.0' encoding='UTF-16'?><html></html>"
input = BytesIO(content.encode('utf-16'))
tree = ElementTree()
tree.parse(input)
# Write content
output = BytesIO()
tree.write(output, encoding="utf-16")
assert output.getvalue().decode('utf-16') == content

Here is a patch which solves the problem of writing ElementTree with utf-16 or utf-32 encoding.

Anyone can review the patch?

The patch needs some tests.
Also, it seems that ElementTree.write() will only accept files inheriting from io.IOBase, where a only a .write() method was expected before. Is it the case?

Here is updated patch, with tests and support of objects with only 'write' method.

It would be nice to fix this bug before forking of the 3.3.0b1 release clone.

I will try to find time to review it before the fork, but since time is tight I don't promise.
That said, this patch falls more into the bugfix category than a new feature, so I think it will be OK after beta as well.

Serhiy, note that _SimpleElementPath is now gone in 3.3, since ElementPath.py is always there in stdlib. Could you update the patch to reflect this?
Another thing. I'm trying really hard to phase out the doctest tests of etree, replacing them with unittest-based tests as much as possible. The doctests are causing all kinds of trouble with parametrized testing for both the Python and the C implementations. Please don't add new doctests. If you add tests, add them to existing TestCase classes, or create new ones.

> Serhiy, note that _SimpleElementPath is now gone in 3.3, since ElementPath.py is always there in stdlib. Could you update the patch to reflect this?
Don't worry, _SimpleElementPath is not used in changes.
> Another thing. I'm trying really hard to phase out the doctest tests of etree, replacing them with unittest-based tests as much as possible. The doctests are causing all kinds of trouble with parametrized testing for both the Python and the C implementations. Please don't add new doctests. If you add tests, add them to existing TestCase classes, or create new ones.
Done. I replaced the encoding doctest by unittest-based tests and merge
it with StringIOTest and user IO tests in one IOTest class. Added test
for StringIO writing.
Also I've improved support of unbuffered file objects (as for
issue1470548).

Thanks for your work on this, Serhiy. I made some comments in the code-review tool, mainly about the complexity of the resulting code. 
Great work on switching the tests to unittest, much appreciated.

Here is a patch with using context management (as Eli advised). This
makes error handling much safer and probably makes the code a little
easier. Several new tests are added.

Thanks, this looks much better. I've reviewed the _4 patch with some minor comments.

Serhiy, can you also take a look at #9458 - it may be related?

Patch updated with some comments.

New changeset 6120cf695574 by Eli Bendersky in branch 'default':
Close #1767933: Badly formed XML using etree and utf-16. Patch by Serhiy Storchaka, with some minor fixes by me
http://hg.python.org/cpython/rev/6120cf695574 

Thank you, Eli.
However changes to tostring() and tostringlist() break the invariant b"".join(tostringlist(element, 'utf-16')) == tostring(element, 'utf-16'). You should add followed methods to DataStream:
 def seekable(self):
 return True
 def tell(self):
 return len(data)
Note, that monkey-patched version is faster.
 stream = io.BufferedIOBase()
 stream.writable = lambda: True
 stream.write = data.append
 stream.seekable = lambda: True
 stream.tell = data.__len__
Benchmark results:
tostring() with BytesIO:
$ ./python -m timeit -s "import xml.etree.ElementTree as ET; e=ET.XML('<root/>')" "ET.tostring(e, 'utf-16')"
1000 loops, best of 3: 268 usec per loop
$ ./python -m timeit -s "import xml.etree.ElementTree as ET; e=ET.XML('<root>'+'<child/>'*100+'</root>' )" "ET.tostring(e, 'utf-16')"
100 loops, best of 3: 4.63 msec per loop
tostring() with monkey-patching:
$ ./python -m timeit -s "import xml.etree.ElementTree as ET; e=ET.XML('<root/>')" "ET.tostring(e, 'utf-16')"
1000 loops, best of 3: 263 usec per loop
$ ./python -m timeit -s "import xml.etree.ElementTree as ET; e=ET.XML('<root>'+'<child/>'*100+'</root>' )" "ET.tostring(e, 'utf-16')"
100 loops, best of 3: 3.84 msec per loop
tostringlist() with DataStream class:
$ ./python -m timeit -s "import xml.etree.ElementTree as ET; e=ET.XML('<root/>')" "ET.tostringlist(e, 'utf-16')"
1000 loops, best of 3: 624 usec per loop
$ ./python -m timeit -s "import xml.etree.ElementTree as ET; e=ET.XML('<root>'+'<child/>'*100+'</root>' )" "ET.tostringlist(e, 'utf-16')"
100 loops, best of 3: 4.09 msec per loop
tostringlist() with monkey-patching:
$ ./python -m timeit -s "import xml.etree.ElementTree as ET; e=ET.XML('<root/>')" "ET.tostringlist(e, 'utf-16')"1000 loops, best of 3: 259 usec per loop
$ ./python -m timeit -s "import xml.etree.ElementTree as ET; e=ET.XML('<root>'+'<child/>'*100+'</root>' )" "ET.tostringlist(e, 'utf-16')"
100 loops, best of 3: 3.81 msec per loop

Fixed the invariant violation in changeset 64ff90e07d71
I'll review the performance difference separately

I posted a message to python-dev about the performance issue

New changeset 51978f89e5ed by Eli Bendersky in branch 'default':
Optimize tostringlist by taking the stream class outside the function. It's now 2x faster on short calls. Related to #1767933
http://hg.python.org/cpython/rev/51978f89e5ed 

How about porting this to 3.2? The main difficulty I see with the tests, which significantly differ in 3.2 and 3.3.

Frankly, I don't think the problem is serious enough to warrant a backport to 3.2, given that 3.3 gonna be out in a few weeks. The issue was open for 5 years without anyone seriously complaining :)

Python 3.2 currently shipped in last Ubuntu LTS and will be in production at least next 5 years. I think it will be main Python version for many years.
Here is a compound patch (changesets 6120cf695574, 64ff90e07d71, 51978f89e5ed and 63ba0c32b81a) for Python 3.2 without tests. It is almost same as for 3.3, except using manual finalizing instead ExitStack.