The biggest problem with the BBC is some of its major reporters such as Laura Kuenssberg, Robert Peston, Andrew Marr, Nick Robinson, Hugh Pym, Fiona Bruce etc. These people all have a right-wing bias and Kuenssberg and Peston are so far up the Tory part arse that it reflects very badly on the whole of the BBC. Kuenssberg should have been sacked for some of her mindless reporting during the election. Fiona Bruce openly admitted that BBC Question Time had a right wing bias because it reflected the way the country voted, which is no excuse what so ever.
I wouldn't say the BBC is overtly right or left wing but the government of the day does influence the way the BBC leans politically, so I don't feel it is entirely unbiased either. If they cleared out all of the above right-wing presenters and had more level headed and honest presenters such as Emily Maitlis then I would feel more able to trust what I read and hear from the BBC.