MIX also is supposed to have private messages, so some UI will need to be developed for that. I think that marking messages as "private" would be enough.

After some consideration (and usage) - having a two direction (i.e. possibility to reply via private message and not only receive them) would be helpful

I checked Version 4.0 (79) and the only indication of private/direct message is addition of "From nick@muc.domain". Private messages send from Beagle have in the header "To (private message)".

Which client have you used for testing? I’ve used Conversations as Psi was not properly marking PM (according to the MUC XEP).

Psi was not adding ‚x’ element and causing this issue.

With proper PM sent from Psi comsole, everything was working fine.

I used Psi, but the specification, contrary to what you say, doesn't mandate presence of <x/>, Sending a Private Message says:

To allow for proper synchronization of these messages to the user's other clients by Message Carbons (XEP-0280) [19], the sending client SHOULD add an element qualified by the 'http://jabber.org/protocol/muc#user' namespace to the message. Note: because this requirement was only added in revision 1.28 of this XEP, receiving entities MUST NOT rely on the existence of the element on private messages for proper processing.

Ok, so it is not possible to distinguish PM from normal 1-1 message on the client side if client is not joined to the MUC room. Yet, somehow everyone expects special parsing and treatment of does messages. Generally, I should say that this is not possible to be implemented properly as behavior will change depending on what you you client knows.

I've made a few adjustments to reflect XEP more closely, so it may behave better, but I'm still pretty sure that there will be issues with this feature (as it is not possible to distinguish 1-1 message from PM message without knowledge that messages came from the MUC room).

New version at dropbox.

It indeed does works better.