The following also avoids the temporary file, and the use of cat. Oh, and the use of cut.
find $PATH -name "*.C#" -newer "abc.C#1234" -print |
while read file; do
awk '/Subject/ { s=substr($0,1,35) } /Date/ { d=substr($0,68,53) } END { print s, d }' "$file"
done
The main thing here really is (1) use an output format which does not include a newline between the items you want to print (I used a space instead); and (2) for efficiency and elegance, combine all the processing into a single awk script.
If Subject always comes before Date, you could do away with the while loop, too.