After some time I figured out the problem. As I sad previously I suspected that problem was that DP started using C partition for storing packages.
For some reason, and I still don't know why, when DP start's to use some other partition other than first used partition this problem with hash mismatch/missed files occurs and you cannot use any of those packages.
I manage to fix it by preventing DP to store packages on my C drive.
In order to do this you have to create blank txt file called NO_SMS_ON_DRIVE.SMS on the root of the drive on witch you don't want any packages created. After that you have to delete those faulty packages and redeploy them. After redeploying them, you have to select update distribution point option on every of those packages, and only after that they are OK.
I don't know if this is something that has to do with my configuration or it's just a bug which has to be resolved by Microsoft in the future, but the important thing is that there is a solution for now.
Thank you all for your replies, and I hope this will be helpful to someone else.