Hang on - hold the phone.
Acting is what I *do* know about. From a purely qualitative perspective, Tate not researching the series beyond her role is *exactly* what the very best actors should do (not that this is why she did it, necessarily). Donna doesn't know anything about the doctor beyond what she experiences with him, therefore to play her more convincingly, more in line with Stanislavski's 'system' (or the Method, as it went on to be developed in the States), researching the series is not only unnecessary, it would be actively harmful. As a fan you might be offended that she has never been into Who as a wider entity than the role she played - but there's bugger all reason why an actor *should*.
I love that Buzzcocks episode. Yes, she's completely fucking clueless - though she plays up to it, and it's obv part of her offscreen personality... I also suspect she's a bit pissed... but Tennant (a massive Who geek) clearly adores her for it. They went on to do Taming of the Shrew together in the west end. It received rave reviews. I fully expect that Tate doesn't know a great deal about Shakespeare or the canon. She didn't need to, though, even if i think it's really interesting. As an actor she needs to know one part really well. That's all.
Donna is an extraordinary companion. Far and away the best of new Who. Mostly that's the scripts - but they were created for her, the plot arc written with her in mind after working with her on the runaway bride a year earlier. Her delivery is... full on. Probably quite annoying, in some ways (appropriately to the character)... but the emotional pitch varies throughout the series and the stuff at the end is nicely at contrast with the comic overstatement at the start.