I would like to see my average score on each hole of my home course, so it be compared to the course handicap. Or any course that you have enough scores to be statistically valid. It could be as simple as an extra row on the score card showing your scoring average on each hole.

I agree with this. I think it would be awesome to see scoring averages per hole for courses where you have played multiple times.

Another possibility I think could be interesting as well to see how club choice from the tee affects scoring average. You collect that data already and I imagine you had something like that in mind when you added it.

would love to see it as well

I agree with this too. I used to use another site for score tracking that did this. It's a good feature.

I think that would be very cool to see a list of your worst and best holes. Maybe have a list of scoring averages with course name and hole. and maybe be able to sort based on 3 to 5 scores posted to get a better idea of how you fare on a particular hole.
I also like helfon's idea of how a particular club from the tee effects your score, even par 3/4/5 averages per club.
I know some clubs won't be applicable on certain holes, but I've hit driver on par 3's and 5 irons off of par 5's.

Just a few stats to help give an idea of course management.

we now have a hole-by-hole report for courses that you play multiple times. It doesn't have a name yet and is listed under "New Report" on your game page.

this is great and it makes playing the same course multiple times more fun. one thing i wish it had was a column for over under par. if you average a 4 and it's a par 3 then that hole would be a +1. if you average a 3.4 on a par 4 then that would be a -0.6.

when you click on the column header it should sort the over/under par stat and you would quickly see which hole is hardest and which is easiest for you.

in my example the -0.6 would come first then +1 etc. the way it is now all the par 3's have the lowest score b/c duh! you are supposed to make it in 3 shots, even though they are harder holes with a bigger over/under number than some of the par 4's, 5's.

(ryanlowdermilk suggested this on the comments section when hole by hole scoring was released.)