Is it possible to record incoming parameter values in a procedure call while tracing in SQL Server Profiler?
I'll bite the bullet and tell you that such a trace cannot be set up, because it is not the [perceived] purpose of traces. I have always done it this way:


  WHILE (@@FETCH_STATUS = 0) AND
   &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ( @About80MoreBooleanExpressionsHere)
   BEGIN   /* 1 */
   &nbsp; &nbsp; -- about 700 lines of logic, math and if-parameter-this-then-that
   &nbsp; &nbsp; -- stuff omitted
  &nbsp; &nbsp; &nbsp; INSERT InnerProcedureCallWithinLoop__TraceTable
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;                           VALUES (@from_locn, @About53PARAMSOMITTED
  &nbsp; &nbsp; &nbsp; EXEC  @ConsiderItem =
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; InnerProcedureCallWithinLoop
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; @from_locn,
  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; @About53PARAMSOMITTED,
                                                      ...


If I know that it is only ever called from one location.  Otherwise, I do it in the callee instead of the caller.

ALTER PROC InnerProcedureCallWithinLoop
    @from_locn int,
    @About53PARAMSOMITTED ...
AS
SET TRANSACTION ISOLATION LEVEL READ UNCOMMITTED;
SET NOCOUNT ON;
INSERT InnerProcedureCallWithinLoop__TraceTable VALUES (@from_locn, @prm2, @prm3....
--- rest of proc


This is obviously different from using a trace, which is able to capture events even if they started and never finished (faulty parameters, rolled back transactions).  If that is your problem, you need to look at CLR or email methods to externalise the captured output.