Good start, thanks a lot for the work you put into your comment! Harsh critique follows.
1, 6 and 7 are precise enough to be part of a formal leveling scale. (But we'd need to i18n-ize them a little because all three use the American cultural assumption. I don't know offhand the weight of a pound, the length of a mile, or the number of words in the Gettysburg address :-))
3 could be made more precise with a little work. I'd prefer it to say "write and run a program", to make the winning condition clearer. Also I'd rather use one of the classic examples, e.g. Hello World, 99 bottles of beer on the wall, or any of the first ten Project Euler problems. IMO we shouldn't be in the business of inventing new exercises that teach programming!
2 is not very informative: if you were able to initiate a conversation with a stranger once, that doesn't mean you can do it again. Same for 4: can Bob qualify for level 1 if he's pretty sure he worked for two hours straight at least once in the last month? I'd like to have criteria that are about as informative and insensitive to flukes as #1.
5 and 8 are too vague and need to be completely rethought, IMO. A level 0 person doesn't know what a proper mathematical proof or a proper piece of evidence feels like.
Agreed on substituting Project Euler problems. (God, I should really be doing those at some point...)
Maybe 2 and 4 need to add a frequency requirement? Let's say, in a month, 4 invites and 2 days a week that involve a 2-hour sprint of work. (BTW, I think meeting strangers is less important than initiating conversations with people you've already met; my "social" criterion was about the latter. Can you ask that guy you know from class if he wants to meet up and study? People who can't arrange to meet are at a disadvantage, and I've struggled ...
I just got this random idea that people who want to become better at life could benefit from a common scale of "leveling". No, I don't mean vague Lesswrongey things like "changing your mind". I mean a set of concrete criteria like "you qualify for level 2 if you can do 5 pull-ups, have solved 30 Project Euler problems, and did 10 cold approaches". Obviously there would be separate ladders for different character classes, but not too many. Also obviously, my example was a bit too high for level 2. So I guess I really want to ask some meta questions here:
1) Do you think agreeing on a common leveling scale would be a good thing for a substantial subset of LW users? Would you feel good about leveling up and telling other people about it on LW?
2) Is there some good way to determine leveling criteria that are neither too high nor too low? Maybe make an intermediate scale of "experience points"?