I'd be surprised if they looked at your application again but they might like a gutsy approach - it depends on the role and the manager. When I recruit, I want to find the right person and if I did, I wouldn't re-advertise. It's expensive, time consuming and takes you back to the start of the recruitment process again so don't take rejecting potential candidates lightly.
If you did apply again, I'd make it clear that you feel you didn't give a good representation of yourself.
It sounds like using something like the STAR technique would be helpful. Read more www.interview-skills.co.uk/competency-based-interviews-star.aspx there.
If they're looking for evidence, I'd imagine they are using competency based questions. So say, they asked
- can you give me an example of how youve worked in teams?
And you replied along the lines of "I really like working in teams. I've done it lots".
That wouldn't show evidence.
Using STAR (Situation, Task, Action, Result), you'd say
"when I worked at Acme Industries, I was part of the Widget Team. We had to deliver a large order to a very tight deadline for customer x. We discussed how we would get the extra work done and I suggested we split it into chunks and each do a chunk then share the remaining parts. I finished early so helped me colleague with her chunk as she was struggling to complete it in time. I felt very proud of my contribution to the team, especially because we got the order finished in time and the customer was very happy."
So to break it down
situation - when I worked at Acme Industries, I was part of the Widget Team
Task - We had to deliver a large order to a very tight deadline for customer x
Action - We discussed how we would get the extra work done and I suggested we split it into chunks and each do a chunk then share the remaining parts. I finished early so helped me colleague with her chunk as she was struggling to complete it in time
Result - I felt very proud of my contribution to the team, especially because we got the order finished in time and the customer was very happy."
This gives the recruiter "evidence" that you've worked in teams and gives you a structure to communicate that avoids waffling.
Good luck