We should be able to fix this by using null seperators (although I have not tried it), e.g.,
find -type f -print0 | xargs -0 touch --date="$REFERENCE_DATETIME"
Do you happen to know which files in ESR 38 have spaces? We have not noticed a problem with the updater yet, although previously Mozilla's MAR file generation scripts had problems handling paths that contained spaces (Kathy and I tried to fix those problems when we made the original updater changes for TB, just in case).
browser/components/migration/tests/unit/Library/Application%20Support/ caused this ticket. I have not checked systematically whether there are more instances in the tree now.
For the record, running a find command on an esr38 tree reveals the following (all part of various tests):
./browser/components/migration/tests/unit/Library/Application Support
./browser/components/migration/tests/unit/Library/Application Support/Google/Chrome/Local State
./layout/reftests/fonts/sil/Scheherazade-R 2012-07-03c.ttf
./media/webrtc/trunk/tools/gyp/test/win/command-quote/bat with spaces.bat