Should I correct a course assignment that I already presented? I'm not sure whether the professor will notice the error
How can these affect our/my grade?  



If you do not present the error, it can only be negligible or negative.  I do not see a positive outcome without additional influence.



  Should I contact the professor after correcting the error?  



You state that the next line of communication will be at the Final?  The Final would be too late.  If you're going to do it, then time should be of the essence.  



  Should I correct the work?  



That wholly depends on what the professor would want.  Write a brand-new report?  No.  Show that you understand what the issue was, how it happened, and what a 'fix' would entail?  To the best of your ability, absolutely.  You're presenting a problem, and giving a solution -- not presenting a problem, and expecting a solution on a silver platter.

Regardless of if the professor noticed the error, it would be unwise to punch enough holes in your presentation to render it invalid while you're giving it.  

I've messed-up on some trivial components before.  Communication works wonders.  If you're unhappy with the turn out after working-it-out; then take it to someone else.

Good luck.