OK, what USAFRet says is true - more cautious, but a very good way to avoid the risk of copying errors. If OP is willing to do a complete re-install (says he / she is), this will work well. In fact, since the old HDD is still working and you CAN successfully copy "everything" from it, you should lose nothing. When you use the Copy operation, it will not copy any Bad Sectors, so that's how you avoid unrecognised errors.
Remove the old HDD so only the new one is installed, then do the fresh Install on it, then Install all your application software on it. Yes, you must Install those, not just copy the old apps from the old HDD, so the new Registry has required info on all those apps. Then you re-install the old HDD temporarily and copy all your old data files over. Un-install the old HDD and set it aside in a safe place just in case you forgot something.
AFTER you have your machine working well and are completely satisfied that you have all your old files copied over you can decide what to do with the old unit. Some would just throw it out on the argument that it is old and has shown some errors, so more are coming soon. Alternatively, you can download and use a set of HDD diagnostic utilities from Seagate, the makers of your old HDD - they are called Seatools. Install them on your machine, re-install the old HDD, and run the tests to determine just how much is wrong on the old unit. If you decide only minor things are wrong and can be ignored, I suggest you use the Zero Fill utility on the OLD drive ONLY - make SURE which drive you fill! It will destroy ALL the contents of that unit! But it will also force an internal routine that tests and "corrects" (actually, replaces bad sectors with good spares) the drive so that it is almost like brand new and working well. That is, of course, IF the other tests have already told you there is not much wrong to fix. Once you do that, it is a new empty drive that will need to be Initialized so you can use it for data.
A final note: that Seatools utility package is not really suitable for use with HDD's NOT from Seagate. So if you do this and then decide the old HDD is junk so that you no longer have any Seagate HDD around, just un-install Seatools from your system.