There are two main problems that arise (and a host of others) with a transmitter and receiver placed close together.
The "noise" you mentioned when placing walkie talkies together is due to simple audio feedback - an audio signal from the speaker on the receiver being picked up by the transmitter's microphone - resulting in some "positive" feedback which results in howling or squealing most often. For this scenario, disconnecting the speaker or muting the receiver will usually stop the interference.
The second most common effect is overload of the receiver which happens if the receiver and it's front end, AGC, etc. are not designed for the high signal strength that occurs when the receiver's antenna is so close to the transmitter, thus coupling a very high signal level into the receiver. The only way to combat this is to reduce the coupling between the devices (shielding the antennas from one another, removing the receive antenna, dropping the tx power, etc.).
The other things that can happen can be more complex, with things like the transmit signal begin coupled into the LO and IF stages in the receiver, etc. The extent and side effects of this type of thing will vary greatly with the design and function of the devices being used.