Uhm, I guess we should call this topic "half-solved"
as it is just a way around the problem, not necesserly and entirely solving the problem of Community Builder and K2 coexistence. I experienced the same problems as many people mentioned on this forum and unfortunately there was no complete answer. Maybe I will share my experience so that some of you may use.
As I use CB login module for loggin in on front end, I noticed that each time user tries to register, he/she gets info that data entered from captcha does not match although no captcha plugin was used. Someone mentioned to disable K2 user plugin, but simpler solution that worked for me was to disable the captcha in K2 (sorry for translation - my site use polish and don't know the exact translation to english) - Options> Additional (extended?) options > enable reCaptcha in register form SET TO "NO".
I also experienced problems with link to "create article" in K2 (not Joomla native editor) in front end (403 error). The solution, in my case was simple - user was not assigned to any "K2 user group" as I simply hadn't created any. As soon as I created K2 user group for "author" and assigned users to that group, the problem stopped.
I didn't find "clean" solution for assigning new users to K2 groups, so I used solution mentioned here:
www.joomlapolis.com/forum/146-general/200500-new-users-not-assigned-to-k2-group?limit=6&start=6
Currently I (again) turned on the community builder integration in K2 settings (some posts suggested it causes problems) and my K2 user plugin is again published but as "first one" with -100 (negative value) value in ordering.
For now it seems to be working, but I am not saying it is 100% working - I guess there may be some issues I simply haven't noticed so far
Edit: Now I noticed that community builder integration in K2 makes my Joomgallery very unhappy - I lost detail view of the picture and so far no sollution for that. I guess I will have to give up - what is CB for when it can not be integrated (and unfortunately I can't give up K2).