(there were more similar errors, I copied only distinct). After brief investigation and googling I found that some time this error can be fixed by disabling script compression. It can be done by adding the following line into web.config:
And it helped. After I added this line into web.configs on all WFEs error disappeared. Users with other browsers also still work without problems. Hope it will help you if you will encounter with similar problem.
Update 2012-06-27: another way to fix this problem is to add site to the Local Intranet zone in IE settings. After that functionality also worked without problems even after we removed scriptResourceHandler from web.config.