Update: I disassembled my melodica and performed surgery proposed by Alan. Really, the air now goes far easier when vent button is depressed – btw. I feel bit lost in English here trying to understand the difference between “pressed” and “depressed” 🙂
Now some condensation could be blown out through the hole near the button, however still far more could be shaken out (and yet significant amount could be seen inside on the plates when disassembled) – so probably it is just less or more normal (as someone at music.stackexchange proposed) for this instrument.