The following parts of tramp-test04-substitute-in-file-name are failing
on Cygwin (and probably also on MS-Windows, but I can't easily test
that):

(should
    (string-equal
     (substitute-in-file-name "/method:host://foo") "/method:host:/foo"))
(should
    (string-equal (substitute-in-file-name "/method:host:/path///foo") 
"/foo"))
(should
    (string-equal (substitute-in-file-name "/method:host://~foo") "/~foo"))

Here are the corresponding evaluations:

(substitute-in-file-name "/method:host://foo")
"/method:host://foo"

(substitute-in-file-name "/method:host:/path///foo")
"//foo"

(substitute-in-file-name "/method:host://~foo")
"//~foo"

This is a consequence of the fact that Tramp calls
substitute-in-file-name on the local part of the file name:

(substitute-in-file-name "//foo")
"//foo"

(substitute-in-file-name "/path///foo")
"//foo"

(substitute-in-file-name "//~foo")
"//~foo"

"//" has a special meaning at the beginning of a file name on Cygwin and
MS-Windows; see the comment near the beginning of
search_embedded_absfilename.  So I don't think there's a real bug here.
Maybe the expected result of the test should simply be adjusted, as in
the attached patch.  Someone who builds on MS-Windows would have to
check this.

Ken