Thanks, Howard, for answer.
What I did and what were the results:
1. Turned on "DEVELOPER: extra Moodle debug messages for developers" and set debugdisplay to YES --> no errors, no warnings, nothing unusual
2. With the moodle/course:view capability all is ok --> for the necessary roles this capability was set up
3. Then I considered what I have done with roles in general. This is the right question!
Deeper situation description: we have implemented role capability "moodle/course:enrolled" (http://tracker.moodle.org/browse/MDL-11798
) in our Moodle. To implement this capability, local changes to database should be done. After setup this capapility all was ok and worked as expected.
Problems started after Moodle update from Moodle 1.9.5+ (Build: 20090902) to Moodle 1.9.5+ (Build: 20091007). During this update changes to database was done and as a result capability "moodle/course:enrolled" was lost.
The problem of forwarding from "Participants view" to "Assign roles" view was because of missing this capability. When restored all went ok!
But there is an open question. How to ensure that after database update the locally added capabilities remain?