First of all, the technical issue of not being able to send the code back (with feedback) needs to be solved. One quick solution would be for the TA to simply insert their comments in the student's code in the submission system. A simple script can then be written that sends the student's submitted work back to them in an email. These can be added to the archive and the effectiveness of the feedback can thus measured and the content of the feedback can be saved for future(possibly automated) use.
One option is that a list of common mistakes can be generated by an experienced instructor or group of instructors and TAs. They can explain these common mistakes in a document that TAs for the course are to spend reading. The common mistakes will be listed for the students online. Whenever a common mistake is made the TA is obliged to recognize it and simply note ``mistake number x has been made on your paper"
Using the archive we can also generate a list of common mistakes. Given a list of previously turned in assignments and their grades we can try to find the difference in code which caused the lower grades.