Easily such an application can be installed in devices that run on Windows Mobile. There are also similar apps for iPhone.
How to determine that the phone has a built in "bug"? Inexperienced at this part of the user to learn about it very hard, however, there are some characteristic features, which can determine that the phone is tapped.
For example, a symptom can serve as a strong heating of the phone battery. When the battery is too hot, it suggests that it is discharged. If this happens during a long conversation, then that's fine. Another thing, if the mobile phone is not used for a few hours, and the battery is hot. It tells about what's inside the device some kind of a problem. Option: for example, running a spyware application.
Another sign of the presence of a mobile device spyware application may be a delay in the process on/off. It is also worth paying special attention. Although, if the mobile phone turns on/off longer than usual, this may also be the usual technical problems.
Also should be alerted of the suspicious behavior of the mobile device. In other words, when it starts to "fail": to switch the display illumination, you can install applications either constantly rebooted. In this case, the mobile phone is likely infected. However, we also cannot exclude possible failures in the operating system.
Another suspicious characteristic is interference. Moreover, interference can be of two types:

interference that can be heard during a call (echo, other suspicious noises that accompany your conversation.

interference arising from the presence of the mobile device, for example, near the speakers. These disturbances occur when the tip of the antenna of the phone to other devices (typically, column loudspeakers). When this sound is heard from the speaker during a call, that's fine. Another thing, when this sound is present all the time, including when the phone is not active. This symptom may mean that the spyware application transmits any data.