It is possible for a transmitter to interfere with nearby electronics, anyone who's held a GSM phone near their hifi has probably heard the characteristic noise it makes.
All electronic kit that has regulatory approval is tested to check that it is immune to such interference, up to a given field strength. For consumer kit that's usually 2V/m, for vehicles I think it's 50V/m. I don't know if aircraft are considered to be vehicles or whether there is a more specific standard, but there should be a documented set of tests on an aircraft with the equipment fitted.
However, it is always possible that limits can be exceeded, there are tales of the road past RAF Fylingdales where vehicles would misbehave if the radar was operational, and field strengths in excess of 50V/m have supposedly been recorded. That's over 6.6W/m^2 when expressed as a power density. A mobile phone doesn't put out much power, but if it happens to excite a resonant structure, it can generate quite a high field strength. One cannot be sure that there isn't such a structure, which could be a bit of metal trim on a suitcase in a particular place in the hold close to some of the internal wiring. A possible hole in the cheese.
There is also the fact that the test sample passed, but if someone missed a bolt, or a bit of corrosion has occurred in the wrong place, a production unit may be susceptible to a bit of RF power. One would hope that with all the checks on aircraft that this is unlikely, but for corrosion to be found it has to exist for some time between checks. It's another hole in the cheese.
On a purely practical note, GSM has a speed limit. If you're flying towards the phone mast at 500mph then it's not going to cope too well, although one off to the side will have a lower relative speed and it's going to work. If you're sticking to lower speeds under FL100 then you'll probably get away with it down that low.
To finish on a personal note, I think anyone wanting to use a mobile phone on an aircraft should be aware that the fuselage is going to degrade the signal, and also that other passengers may not appreciate the phone use, and so go outside to make the call.
