Well, despite my loving Doctor Who fanfiction, the almost national cliche for them is that the companion meets the Doctor, and then they fall in love with the Doctor. My other problem is that pretty much 99% of Doctor Who fanfiction has spelling and grammar errors--and sometimes, it's impossible to read! Those are my two MAIN problems. I have plenty more, but I can't fit them into 2000 characters.
The only fanfiction I didn't have a single problem with was a one-shot that had a really unexpected end.