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The handler for the "Trailing garbage" error for "uu-codec" uses Python 2 code, while the copy in the "uu" module has the correct Python 3 code.
Please change the line at
https://hg.python.org/cpython/file/775453a7b85d/Lib/encodings/uu_codec.py#l57
to look like
https://hg.python.org/cpython/file/775453a7b85d/Lib/uu.py#l148
In particular, drop ord() and use floor division. Better yet, maybe the code could be reused so that there is less duplication!
Demonstration:
>>> codecs.decode(b"begin 666 <data>\n!,___\n \nend\n", "uu-codec")
Traceback (most recent call last):
 File "/usr/lib/python3.4/encodings/uu_codec.py", line 54, in uu_decode
 data = binascii.a2b_uu(s)
binascii.Error: Trailing garbage
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
 File "/usr/lib/python3.4/encodings/uu_codec.py", line 57, in uu_decode
 nbytes = (((ord(s[0])-32) & 63) * 4 + 5) / 3
TypeError: ord() expected string of length 1, but int found
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
TypeError: decoding with 'uu-codec' codec failed (TypeError: ord() expected string of length 1, but int found)
>>> codecs.decode(b"begin 666 <data>\n!,P \n \nend\n", "uu-codec")
b'3' # Expected output for both cases

Do you want to provide a patch Martin?

Here are two patches: a test and a fix. I’m not sure if it is okay to add a test for the "codecs" module with the tests for the "uu" module; it was easier that way because I am basically running the same test over the two different APIs.

New changeset ad89a652b4ed by Serhiy Storchaka in branch '3.4':
Issue #22406: Fixed the uu_codec codec incorrectly ported to 3.x.
https://hg.python.org/cpython/rev/ad89a652b4ed
New changeset b18ef4a3e7c1 by Serhiy Storchaka in branch 'default':
Issue #22406: Fixed the uu_codec codec incorrectly ported to 3.x.
https://hg.python.org/cpython/rev/b18ef4a3e7c1
New changeset 7b82b58b8329 by Serhiy Storchaka in branch '2.7':
Backported tests for issue #22406.
https://hg.python.org/cpython/rev/7b82b58b8329 

I think it is safer now just fix existing code than replace it with totally different code with the risk of incompatibility. In any case uu_codec needs rewriting because currently it doesn't support incremental encoding and decoding.
Thank you for your contribution Martin. And if you are going to do further contribution, please submit a contributor form (https://www.python.org/psf/contrib/).
Few notes. It is more handy to provide all changes as one patch. And your patches contain trailing spaces in blank lines.