There are numerous threads on this in the Tech section of the forum. You might want to check to see if any of the advice there helps you.
There is, apparently, going to be a new Patch tomorrow which will "hopefully" resolve many of these issues.
STO is about my Liberated Borg Federation Captain with his Breen 1st Officer, Jem'Hadar Tactical Officer, Liberated Borg Engineering Officer, Android Ops Officer, Photonic Science Officer, Gorn Science Officer, and Reman Medical Officer jumping into their Jem'Hadar Carrier and flying off to do missions for the new Romulan Empire. But for some players allowing a T5 Connie to be used breaks the canon in the game.
I've been having the same problem as well, at first I thought there were registry errors since most of the files it says are damaged are .dll files. Hopefully tomorrow's patch will fix this.
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There is, apparently, going to be a new Patch tomorrow which will "hopefully" resolve many of these issues.