So many answers - thank you guys, very much!
After studying all posts I came to a conclusion that my problem with cell phones was not their use by players - but the fact that I'm less familiar with phones than my players. =(
No, really. I have a notebook, but my phone is an old Samsung with no Internet connecion at all, and the previous was Sony Ericsson k310i. SO when my players (they are younger than me) started to use their phones' features... Google search, different applications and so on - looks like it... well.. confused and frightened me in some way. I was the Keeper, but hell - I was simply not in charge of the situation! I could not controll the game because I simply didn't know my players' capabilities!
It was something like a chest in Gamers: Dorkness Rising - "... and a Lightsaber! - WHAT???"
As for the points mentioned - I really liked the idea of desinformation and misleading Internet can bring as well as creating a tension through strange posts.
Yet there still are some things that make creating and running adventures a little more complicated.
First, are NPCs. All those librarian, old professors, antiqarians and so on can be swapped with Google search in many cases. Especially it concerns translations - why bother yourself with finding a French-speaking guy when you have google-translate at hand to get the idea of the text? And the problem here is not the quality of the translation - but in excluding of an NPC as a part of game-mechanics.
Of coure situations can be different, but still Inernet can substitute too much NPCs. =(
Second, handouts. It is more difficult (at least for me) to create a false Wiki-page handout, and been printed it looks a little... weird. While good old journal pages are easier to create and are much more atmospheric and impressive.
And third is the total amount of information players can get in one minute - the amount that a Keeper can be unable to present to them!
Something like "I'd like to google about a Golden Dawn order" - and it brings up articles about all its members and followers which in turn is followed by 100 more connected articles and so on. How to deal with it, especially if the information searched is not "How to kill shoggy", but something of a more logical and realistic matter? Say, chemistry articles, medcine - well, anything!