Some of messages are not downloaded correctly.

End of several messages is missing - typically few characters. Examples:

... Botanická 68a 

602 00 Brno 

vs 

Botanická

Alexandra Nyi vs Alexandra Nyitraiova.

I get the same message. Only get the header information not the content

Could be some cache corruption. Right-click on the folder and choose Properties > Repair. If it is a GMail account, you need to right-click on All Mail and choose Properties > Repair.