At first it happened only in some Rhino windows (files), I thought maybe high number of blocks in my document was to blame. This is a new file with only a single (top level) linked block pasted and the bug showed up already as well.
The behaviour is very unpredictable, just after posting this, I opened the same file again in read-only mode by accident, and then a larger working file as well. Block manager suddenly worked in both windows. After closing all Rhino instances and reopening something again, it did not work again.
AFAIK I have only two plugins: VisualARQ 3 and this one from Epic Games (installed only today, while the bug started earlier), I can check it tomorrow.