Postgres incomplete startup packet error
There are 3 different items in this question:


Incomplete startup packet occuring at server start is inconsequential, you may ignore it. Read Incomplete startup packet help needed (in pgsql-general mailing-list) for more.
syntax error at or near "exit" at character 1 means that a client issued exit as if it was an SQL statement.
The could not exec error when issuing service postgresql restart looks like a serious installation problem but it's contradicted by the log entry database system is ready to accept connections meaning that the server started up just fine.