German papers are concerned about racist violence, while the Czech press suspects political motives behind a high-profile punch-up.
Spanish newspapers are exercised by African boat people, and a Hungarian paper ponders the future of Italian football.
Several German papers urge action over far-right violence after a Berlin politician of Turkish origin was injured in a suspected racist attack on Friday.
In an allusion to the official World Cup slogan, "A time to make friends", a headline in Die Tageszeitung asks whether the event will be "a time to meet Nazis".
The paper believes that the neo-Nazi scene may have miscalculated, however, by planning a rally in Leipzig during the Iran-Angola match to "demonstrate solidarity with the Holocaust denier Ahmadinejad".
"Leipzig of all cities!" the paper exclaims. It says far-right demonstrators there have had to contend with powerful counter-demonstrations in recent years.
"Perhaps this is an ideal opportunity to show the world in this very place that it is impossible to stage such a neo-Nazi march," the paper believes.
Under the headline "A disgrace", the Frankfurter Rundschau urges an open debate about right-wing extremism.
"Let us start to deal with right-wing blots in our society openly, so that all people who live here can feel at home and all World Cup visitors can really make friends here," the paper says.
The Berliner Zeitung says the authorities in Berlin should provide visitors with information on which areas they should avoid.
The paper acknowledges that the city's image may suffer as a result of such a move, but it adds that it would suffer even more in the event of a neo-Nazi attack on World Cup visitors.
"How many people have to be injured for concerns over the safety of visitors to outweigh concerns over the city's image?" it asks.
The Czech daily Mlada Fronta Dnes suspects an opposition politician and presidential adviser who slapped Health Minister David Rath had political rather than just personal motives.
"Miroslav Macek is neither stupid nor naive nor inexperienced - he must have known that he would be drawn into a political game," the paper says.
It feels Mr Macek's explanation that he was responding to comments by Mr Rath about him and his wife may not be the whole story.
The paper observes that the slap and subsequent fight between the two men has sparked attacks against his party, the Civic Democrats, and wonders whether this was in fact Mr Macek's intention.
Fellow Czech daily Pravo takes a similar line. Under the headline "Slap's hidden message", the paper interprets Mr Macek's actions as an attack on the Civic Democrats' leadership.
And it wonders what role President Vaclav Klaus, who is also the honorary chairman of the Civic Democrats, may have played.
"Macek would hardly have started such a game without feeling at least a hint of support from Prague Castle," the president's official residence, it says.
Migration to Spain
After a record 647 boat people arrived in the Canary Islands on Friday, Spain's El Pais says the current mass influx of Africans should have been foreseen.
"Neither this government nor the previous ones or the EU were ready to tackle this problem, which is continental and requires European measures," the paper says.
It notes that Spanish diplomats are on their way to Africa in what it regards as a long overdue bid to curb illegal migration, partly by improving people's lives there.
The paper argues that "it is not only up to Spain but to the whole of Europe" to make a serious effort to dismantle protectionism against African produce and to increase development aid.
It says Spain has tripled such aid to 400m euros, but it also backs the government's warning that illegal immigrants will still be repatriated.
Hungary's Nepszabadsag says a scandal rocking some of the top clubs in Italian football may influence the choice of host for the 2012 European Championship in Hungary's favour.
"Italian football is in ruins," the paper says.
It believes allegations of match-fixing, illegal betting and manipulation of referee assignments may cast a shadow over Italy's World Cup performance and may undermine its bid for the 2012 event.
"In the final vote," the paper says, "the current scandal might give an advantage to the joint Croatian-Hungarian bid, or even make it fall in our lap".
The paper warns Hungarians, however, not to be lulled into a false sense of security by assuming that "everything is all right over here".
The European press review is compiled by BBC Monitoring from internet editions of the main European newspapers and some early printed editions.