6th gear is fine normally, but often if I do a 4-6 or 3-6 shift it will grind. I've never noticed it grinding on a 5-6 shift. Is the answer to stop shifting from 4th and 3rd to 6th(which I've been trying to do, but I forget once in a while,) or do I have a synchro problem?
Also, reverse is a bit tough to get into when the car is sitting still. The shifter will go into the reverse position, but does not actually engage reverse sometimes. I have to keep pushing the shifter into R as I let off the clutch to reliably get it into R. It's never popped out once in R though.
Do I need a new tranny? Transmission's are covered to 60k on '04's, right?
Thanks for any help.

 

manual transmissions have always had trouble going into R, no matter what the car is.

try pulling the car out of gear and into neutral, then let go of the stick, then push it into 6th and see if it still does it, there seems to be a built in resistance for 6th gear, maybe part of the reverse lockout mechanism. I don't ever hear grinding going into 6th but I do have a hard time doing it sometimes. if you still hear grinding I'd say take it to the dealership.