I am the lead hardware engineer for Backcountry Access.
Interference from personal electronic devices (PED) is very real, and it can range anywhere from minimal impact to severe. The reasons are a little complicated to understand, but basically the worst case is if the PED emits a signal at or very close to 457kHz, which is the beacon frequency.
LED headlamps could have an internal regulator or dimmer emitting large signals in this band unintentionally. The dimming circuitry can actually make the problem much worse! If you absolutely must have an LED light near the searching beacon, the best thing you can do is to switch it to full brightness, so that the dimming circuitry is less likely to cause problems.
Beacon designers do everything possible to minimize this problem, but we have no control over other electronic devices.
Cell phones and other devices don't intentionally transmit here but they emit broadband noise and other signals which makes it more difficult to hear weak beacon signals. Two way radios, MP3 players, even something like a digital watch or heart rate monitor could emit a signal that interferes. (REALLY!)
"Airplane mode" turns off the radios in the phone, but those are the LEAST of the problem! The processor itself, display, and much other internal circuitry is still on, and can still emit enough signal to mask a beacon unless you are very close.
The nature of the interference will change with different operating modes (play vs standby etc) and as the battery level changes, or at different temperatures, so a device that doesn't seem to cause a problem today can be worse or severe tomorrow.
The best thing you can do is to turn those devices OFF when searching.
The second best is to get those devices away from the search area.
In general doubling the distance from the PED to the beacon receiver will cut the interference by 4x.
An old analog beacon like the Ortovox F1 can be used to illustrate the problem because it allows you to hear what the beacon electronics are trying to deal with. You might find it interesting to grab one cheap on Ebay and have a listen.
From a practical standpoint, the biggest threat is electronics carried by the searchers which can create signals that interfere with the ability of the receivers to hear weak beacon signals at larger distances. Electronic noise emitted by PEDs carried by the victim are not an issue.
In the lab, I can place my cell phone a few inches away from a transmitting beacon. When the beacon is off, my cell phone noise is detectable at about 1.5 meters. Some phones are worse, some are better. With the beacon transmitting, the cell phone noise is completely undetectable during the beacon transmissions. In between beacon pulses, the cell phone again becomes detectable. From a few meters away our to full range, the cell phone will be undetectable while the beacon transmitter will be clear. Get that Ortovox and have a listen!
It is conceivable that PEDs on the victim could, at very short range, confuse the searcher by showing up as a second weak signal.
Metals VERY close to the transmitter (inches) can cause an increase in power consumption in transmit mode, and can distort the field which might cause errors in pinpointing.
When we get into what "could" happen, it can get confusing, and I don't want to risk creating any more myths about how beacons work, but I do want to answer completely and honestly.