I forgot to apply mirror modifier to my model before I parented the rig to the mesh.
I did that afterwards but it made occur some errors with the weight paint.
The screenshot shows my problem especially for the leg. It's weighted for the bone I crossed with red. The other leg is controlled by the very same bone.
The mirrored bone on the other side on the other hand doesn't have any weighted part on the mesh.
Is there any possibility to just transfer the selected faces (as visible in the screenshot) from one bone to an other of the rig?
Or do I have to delete all vertex groups again and re-connect model and rig?
I don't know how you named your bones, but each bone should have been assigned to a vertex group named as the bone. See the mesh "object data" properties tab, under "vertex groups". There you can select/deselect, assign/remove vertices from the selected vertex group.
You can control which vertex is in which group, and eventually remove wrong vertices from the wrong leg group and assign them to the right leg group.
Beware that weight painting can add painted vertices to the selected bone's group.