Quite often any act of retaliation by the IDF against Palestinian actions of terrorism is reported as being provacative or inflamatory (never mind what the "poor defenceless Palestinians" did to illicit such a response).
The fact that young Palestinians are encouraged to attack IDF forces and are sometimes injured or killed also generates sympathy for their side.
Personally I think the fact that the rest of the Arab world is sympathetic to the Palestinians also plays a major part because of their monopoly on oil.
Finally there are many Arab propaganda spin-doctors working full time to convince the press that they are oppressed victims in the whole affair.
Most of the arabs and moslems I have met personally were virulently anti-semetic and in virtually every country in Europe there is a significantly higher population of arabs/moslems than Jews. Therefore their version of events is more likely to be the one being told
And the people that work in the media (usually middle class of left/liberal persuasion)generally have an idealised "picture-postcard" view of Muslims & Muslim culture in general because they don't live amongst them. Ordinary "working class" people who do, generally have a more realistic view.
As for anti-semitism, I live close to area with a large Jewish population in the UK and I can't say I'm aware of any problems. The odd isolated incident maybe.